We report the superconductivity of the CaSn3 single crystal with a AuCu3-type structure, namely cubic space group Pm3m. The superconducting transition temperature TC=4.2 K is determined by the magnetic susceptibility, electrical resistivity, and heat capacity measurements. The magnetization versus magnetic field (M-H) curve at low temperatures shows the typical-II superconducting behavior. The estimated lower and upper critical fields are about 125 Oe and 1.79 T, respectively. The penetration depth lambda(0) and coherence length xi(0) are calculated to be approximately 1147 nm and 136 nm by the Ginzburg-Landau equations. The estimated Sommerfeld coefficient of the normal state {gamma}_N is about 2.9 mJ/mol K2. {Delta}C/{gamma}NTC =1.13 and {lambda}ep=0.65 suggest that CaSn3 single crystal is a weakly coupled superconductor. Electronic band structure calculations show a complex multi-sheet Fermi surface formed by three bands and a low density of states (DOS) at the Fermi level, which is consistent with the experimental results. Based on the analysis of electron phonon coupling of AX3 compounds (A=Ca, La, and Y; X=Sn and Pb), we theoretically proposed a way to increase TC in the system.