Electron acceleration from the interaction of a Gaussian laser pulse with initial axial electron is investigated,using a single test electron model in vacuum. Under the different laser parameters, the electron energy gain depends on the laser intensity, focal spot size and pulse width.The electron energy gain have a optimum focal spot size. There are no evident energy gain when the focal spot size is too big or small. Given the laser intensity,the optimum focal size increases with the pulse width, and the ratio of the optimum focal size to the pulse width is fixed.