As a first part of call you need to monitor and note whether the employee is constantly complaining as this may be a perceptual issue on your part. You may have only had a few interactions with the employee where they complained. However, this is really irked you and you quickly classified them as a moan. This is not fair on the employee so you need to challenge all your assumptions, all the time.
Have a one to one with the employee and ask them directly what grievances they have. Review these complaints with your employee and have a frank and open discussion in regards the legitimacy of their grievances.
If after the meeting, the employee is still complaining about every matter under the sun and poisoning the atmosphere in your office, have another 15 minutes one to one and discuss potential solutions to their grievances. Let the employee suggest a solution and assess whether it is an actual runner. If the subject of most their grievances is a person, you should meet with the other person privately to get their side of the story. It there is a clear standoff, ask the complaining employee to make a formal complaint and get your HR department to act as a facilitator and adjudicate on the issue. Also request that all parties stop gossiping and complaining until the situation is resolved.
It, despite the above process, your employee continues relentlessly in complaining to his/her colleagues, disciplinary action may be the only last resort, especially if their behaviour is in breach of company policy and it there is ample proof that they are harassing other employees and perhaps neglecting their own duties, leading to poor performance. Get legal advice prior to going down the disciplinary route it complaints are relating to something contentious like discrimination (your actions could be regarded as retaliatory). However, if complaints clearly consist of baseless allegations against co-workers, that is a totally different matter.
Constructive complaining should always be welcome. However, continuous and needless moaning and complaining needs to be tackled head on, it you wish to protect positive morale in your workplace.