An irreversible cycle model of a Bose–Otto engine is established, in which finite time thermodynamic processes and the irreversibility result from the nonisentropic compression and expansion processes are taken into account. Based on the model, expressions for the power output and efficiency of the Bose–Otto engine are derived. On the basis of the thermodynamic properties of ideal Bose gas, the effects of the irreversibility and the compression ratio of the two isochoric processes on the performance of the Bose–Otto engine are revealed and some important performance parameters are optimized. Furthermore, some optimal operating regions including those for the power output, efficiency, and the temperatures of the cyclic working substance at two important state points are determined and evaluated. Finally, several special cases are discussed in detail.