Since mold thrives in damp environments, try to find the source of the water that is causing mold on the concrete. Often times, excessive moisture in basements is due to the humidity, in which case you may need to purchase a dehumidifier to minimize the risk of future mold problems.
Seal off the room with plastic sheeting to prevent the spread of mold spores. This includes sealing vents, intakes, doorways and other exit points. Open a nearby window and position a fan pointing outdoors to blow any airborne mold spores outside. Turn off your HVAC system.
Put on your rubber gloves and dust mask for safety. Now apply some household soap or detergent to the moldy concrete, and then thoroughly scrub the effected area with a scrub brush. Clean as much mold as possible with the cleaning detergent or soap.
Apply a mixture of four parts water and one part bleach to the moldy concrete to disinfect the area. Clean up the excess bleach and cleaning solution with disposable rags.
Allow the concrete to completely dry. You may use a fan to speed up the process. It's extremely important to thoroughly dry the area to get rid of all moisture, since mold needs moisture to grow.
Dispose of rubber gloves, used rags, plastic sheeting and any other material used during the cleaning process into a heavy-duty trash bag. Do not carry the trash bag through the house, because it may spread mold spores to other areas of your home. Instead, use the nearest exit (or window) to place the trash bag outside. At that point, you should take the mold-filled trash bag to the nearest landfill as soon as possible.