The Gaussian thermostatting technique has been widely used in constant-temperature molecular dynamics. In this paper we develop operator-splitting integrators for the Gaussian thermostated equations of motion. The new integrators are explicit, very simple to program, and require minimum computer memory. In particular, they can preserve the constancy of the system’s kinetic energy. Numerical experiments show that the present integrators are much more efficient than conventional integrators such as the Runge-Kutta methods. Extension of the integrators to multiple timescale MD simulations is also discussed.