We develop an analytic theory for the recently demonstrated Josephson junction laser [M. C. Cassidy et al., Science 355, 939 (2017)SCIEAS0036-807510.1126/science.aah6640]. By working in the time-domain representation (rather than the frequency domain), a single nonlinear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.