Two-dimensional (2D) SnS has attracted much attention as a phosphorene analogue due to the promising applications in next-generation nanoelectronic and photovoltaic devices. It has a bandgap of 1.3 eV, which is matched very well with incident solar radiation. To improve the switching character of devices, it is significant to modulate the bandgap of 2D SnS. In this work, potassium ion (K+) or calcium ion (Ca2+) is absorbed on the top surface of SnS films to produce an electric field, by which the bandgap can be tuned effectively. By first-principles method we studied the electronic properties and the modulation mechanism of bandgap in detail. The calculated ionization energy and formation energy are 0.41 eV and 0.26 eV for K (1.33 eV and 1.07 eV for Ca). Such little values indicate that it is feasible for ion absorbed on the surface to be used to modulate the bandgap of SnS films. Our calculations also show that the carrier mobility in plane of SnS films has a character of strong anisotropy and the electron mobility is very high in y direction (25.22 × 103 cm2 V-1 s-1 for SnS trilayer). Therefore 2D SnS has potential application in nanoelectronic and photovoltaic devices in the future. We hope our results will motivate experimental efforts of 2D SnS.