In this letter, we present a generalized orthogonal Golay complementary sequence (OGCS) set that consists of multiple subsets, therein, each subset is a conventional OGCS set, and any two sequences from different subsets have three-valued low in-phase cross-correlation (IPCC). At the cost of slight reduction of IPCC performance, the number of sequences in our set is enormously enlarged. When our set is applied to high frequency $M$ -ary spread spectrum communication link with orthogonal frequency division multiplexing modulation, the peak-to-mean envelope power ratio of the transmitted signal can be controlled not to exceed 3 dB, and the data rate can be higher than the one from the existing sequence sets. Finally, the simulation results show a desirable tradeoff between bit error rate and spectral efficiency.