We present a semiclassical Moyal dynamics (SMD) method based on the phase space formulation of quantum dynamics. In contrast to the quantized Hamiltonian dynamics approach by Prezhdo et al. using the Heisenberg equation of motion, SMD adopts the Moyal equation of motion to derive the time evolution of expectation values and uses an auxiliary phase space distribution technique to systematically terminate the coupled equations of motion. Thereby, tedious derivation of commutators is essentially not required, and semiclassical dynamics of arbitrary orders can be realized. The appealing simplicity, flexibility, and reliability of SMD are demonstrated in three representative model systems with strong quantum effects.