A hybrid molecular dynamics-Monte Carlo grand canonical simulation technique is developed for systems with constant chemical potential and temperature. The method ensures that the particle number and energy fluctuate according to the standard grand canonical probability distribution. Partial coupling and fractional particles are used to enhance the success of insertion and deletion attempts, and the method is shown to be feasible in dense liquids. The method is applied to a Lennard-Jones fluid and it gives the density as a function of chemical potential in agreement with known results. It is demonstrated that the transport coefficients can be obtained with the method by analyzing the influence of the stochastic perturbation on the diffusion constant for an isothermal system. (C) 2003 American Institute of Physics.