In this work, we study the correlation between the photon index (Γ) of the X-ray spectrum and the 2-10 keV X-ray luminosity (LX) for black hole X-ray binaries (BHBs). The BHB sample is mainly from the quiescent, hard and intermediate states, with values of LX ranging from ~ 1030.5 to 1037.5 erg s-1. We nd that the photon index Γ is positively or negatively correlated with the X-ray luminosity LX, for LX above or below a critical value, ~ 1036.5 erg s-1. This result is consistent with previous works. Moreover, when LX ≤ ~ 1033 erg s-1, we found that the photon index is roughly independent of the X-ray luminosity. We interpret the above correlations in the framework of a coupled hot accretion flow - jet model. Besides, we also find that in the moderate-luminosity region, different sources may have different anti-correlation slopes, and we argue this diversity is caused by the different value of δ, which describes the fraction of turbulent dissipation that directly heats electrons.