Oscillations are ubiquitous phenomena in biological systems. Conventional models of biological periodic oscillations usually invoke interconnecting transcriptional feedback loops. Some specific proteins function as transcription factors, which in turn negatively regulate the expression of the genes that encode these "clock proteins." These loops may lead to rhythmic changes in gene expression in a cell. In the case of multicellular tissue, collective oscillation is often due to the synchronization of these cells, which manifest themselves as autonomous oscillators. In contrast, we propose here a different scenario for the occurrence of collective oscillation in a group of nonoscillatory cells. Neither periodic external stimulation nor pacemaker cells with intrinsically oscillator are included in the present system. By adopting a spatially inhomogeneous active factor, we observe and analyze a coupling-induced oscillation, inherent to the phenomenon of wave propagation due to intracellular communication.