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These years, two-dimensional (2D) superconductors have attracted more and more attentions. The critical temperature ( T c ) of superconductors can be modified by hole/electron doping, atom adsorption, strain and other means, so as to realize superconductivity with higher T c . In this paper, using first-principles calculations, we study the superconductivity of monolayer hexagonal boron phosphide (h-BP) by metal atoms adsorption. The electronic structure and electron-phonon coupling (EPC) of MBP (M=Li, Na, Ti) are studied. It is found that monolayer h-BP transforms from a semiconductor to a metal after metal atoms adsorption. Based on the conventional EPC mechanism, the coupling between electrons and the out-of-plane vibration of B atoms and P atoms contributes greatly to the EPC. For MBP (M=Li, Na, Ti), the calculated total EPC λ are 1.76, 0.64, and 1.54, and the corresponding T c are 26.38, 6.05, and 14.58 K, respectively. Thus, the predicted MBP (M=Li, Na, Ti) are new 2D superconductors which might be used in future superconducting electronic devices. [ABSTRACT FROM AUTHOR]