On HBR.org, Amy Gallo offers advice on how to handle a pessimist on your team.
She suggests three approaches to negative behaviour:
1) Creating awareness. Pull the team member aside and explain how their comments are received. Once you understand the reason for the negativity you can give them any necessary support.
2) Repositioning negative statements. Don't allow the negativity to fester. Ask the team member for the reasoning behind their pessimism, or for an alternative.
3) Involving the whole team. Singling out a team member in front of the whole team can be damaging. Set team norms and ask everyone to observe them.