What a great question. Keeping fear out of a business environment is like trying to keep an old house from leaking during a storm. Water just seems to find its way in and so does fear. Sometimes team members bring fear in with them from past jobs or childhood experiences. Other times, you may be unknowingly giving off a vibe that adds to their fear. The good news is that there are some things you can do to lower the fear vibe in your workplace:

• Ask people: Now this isn’t as easy as it sounds. If you just start pulling people in your office to ask them what the heck everyone is afraid of…don’t expect much. It’s going to take more effort than that. Select some different groups of people, ones that have been there a while, new ones, various ages, etc. Maybe buy them a good lunch and tell them you really need their help. Go on to tell them that you already know that there’s a fear vibe on the team and that you want to change it. Give them some open ended questions, maybe break them up into small groups. But ask each person/group to be raw and honest about what people are afraid of and why. Ask them specifically for things you do and say that make it worse. Have someone take notes and don’t respond to these answers during the meeting. This is just to learn. Not only will you get some good possibilities; but just the fact that you asked will lower the fear vibe. 
• Err on the side of over communicating: You can either talk openly about sensitive things or your team can do it when you’re not there. Whether this quarter’s numbers are low or a publication is about to drop a negative publicity piece about the company or a key person resigned or got fired, your team needs to know enough from you that they don’t feel like it’s a secret. This doesn’t mean you should disclose personal information about people or that you have to answer questions that are really none of your team’s business. But you can be open about the awkwardness of it and you can give them some of the truthful facts. Maybe you asked a long time leader to leave the team because they couldn’t get on board with your way of treating people. Not only is it true; but it gives you a chance to speak positively about the person you just fired. 
• In public team settings, let the team know you’re working on lowering the fear factor at work. Just saying that out loud lowers it some.
• Spend some time in staff meetings or lunches letting the team ask you whatever they want. Questions about your life, about the early days of the business, about losing a loved one, etc. Make it fun and be enthusiastic with answering their questions.
• Change yo face: Lastly, you get the chance to make dozens of impressions on your team every single day just by passing them in the hall or the lunchroom or the elevator. When you have something on your mind (which is always) and you walk around with this “look” on your face, that looks translates to a new team member that you are bothered that they are even in the hallway at the same time you are, that you definitely don’t want to talk to them and that if you need them for anything, you will shake it out of them. LOOK UP. Smile at people. Hold the door for them. Tell them you’re glad to see them or that you noticed they had a new truck. And if you are serious about connecting with people, make the effort to learn their first names and call them by it. They’ll be blown away.