Golay complementary sets have found many applications in communications, e.g., they have been proposed to control the high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. The relationship between Golay complementary sets and generalized Reed-Muller codes have been proposed to construct Golay complementary sets of length 2m based on generalized Boolean functions. However, the number of used subcarriers is usually non-power-of-two in practical wireless OFDM-based communication systems. In this paper, a new construction of Golay complementary sets of length not equal to 2m based on generalized Boolean functions is proposed. The constructed Golay complementary sets exist for various lengths not equal to 2m and have PAPRs upper bounded by the set size.