This paper describes a theory for mode locking and frequency comb generation by four-wave mixing in a semiconductor quantum-dot active medium. The derivation uses a multimode semiclassical laser theory that accounts for fast carrier collisions within an inhomogeneous distribution of quantum dots. Numerical simulations are presented to illustrate the role of active medium nonlinearities in mode competition, gain saturation, carrier-induced refractive index and creation of combination tones that lead to locking of beat frequencies among lasing modes in the presence of cavity material dispersion.