Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case of sparsely coded patterns, it is biologically important to consider the timings of firings and to study how such consideration influences storage capacities and quality of recalled patterns. For this purpose, we propose a simple extended model of oscillator neural networks to allow for expression of a nonfiring state. Analyzing both equilibrium states and dynamical properties in recalling processes, we find that the system possesses good associative memory.