In this letter, a novel construction of binary cross Z-complementary pairs (CZCPs) based on Boolean functions is proposed. CZCPs have been proposed to be used as training sequences in the spatial modulation system. Due to their zero correlation zone (ZCZ) properties for autocorrelation sums and cross-correlation sums, optimal channel estimation performance over frequency-selective channels can be achieved. In the literature, most constructions of CZCPs are based on existing Golay complementary pairs (GCPs); only one method is based on Boolean functions. However, the length of CZCPs from Boolean functions is very limited. In this letter, the proposed construction can generate CZCPs with more flexible lengths and large ZCZ widths.