Two-dimensional (2D) semiconductors SnP3 are predicted, from first-principles calculations, to host moderate band gaps (0.72 eV for monolayer and 1.07 eV for bilayer), ultrahigh carrier mobility (similar to 10(4) cm(2) V-1 s(-1) for bilayer), strong absorption coefficients (similar to 10(5) cm(-1)) and good stability. Moreover, the band gap can be modulated from an indirect character into a direct one via strain engineering. For experimental accessibility, the calculated exfoliation energies of monolayer and bilayer SnP3 are smaller than those of the common arsenic-type honeycomb structures GeP3 and InP3. More importantly, a semiconductor-to-metal transition is discovered with the layer number N > 2. We demonstrate, in remarkable contrast to the previous understandings, that such phase transition is largely driven by the correlation between lone-pair electrons of interlayer Sn and P atoms. This mechanism is universal for analogues phase transitions in arsenic-type honeycomb structures (GeP3, InP3 and SnP3).