In this paper, we consider the peak-to-average power ratio (PAPR) reduction problem for orthogonal frequency-division multiplexing with offset quadrature amplitude modulation (OFDM/OQAM). In particular, the OFDM/OQAM signal is generated by summing over M time-shifted OFDM/OQAM symbols, where successive symbols are interdependent with each other. The alternative-signal (AS) method, which directly leads to the independent AS (AS-I) and joint AS (AS-J) algorithms, is employed to reduce the PAPR of the OFDM/OQAM signal. The AS-I algorithm reduces the PAPR symbol by symbol with low complexity, whereas the AS-J algorithm applies optimal joint PAPR reduction among M OFDM/OQAM symbols with much higher complexity. To balance the performance and the computation complexity, we propose a sequential optimization procedure, which is denoted AS-S, which achieves a desired compromise between performance and complexity.