A great number of ab initio energy points are calculated using the aug-cc-pV(Q,5)Z basis sets at the multireference configuration interaction level and extrapolated to the complete basis set limit. An exact three-dimensional potential energy surface of the ground-state BH2+ is obtained. A switching function is developed to model the transition of B+(3P) to B+(1S) to guarantee the reliable behavior at B+(3P) + H2(X1∑g+) and BH+(X2∑+) + H(2S) dissociation limits. The various topographic features of the new global potential energy surface are discussed in detail, showing a good agreement with the previous results from the theory. The quasi-classical trajectory method is utilized to calculate the integral cross sections of the B+(3P) + H2(X1∑g+) (v = 0, j = 0) → BH+(X2∑+) + H(2S) reaction, which can provide another support for reliability of the title potential energy surface.