Single photon sources are key devices for quantum communication and quantum computation. Recently, photonic nanowires with an embedded quantum dot have demonstrated to provide remarkable extraction efficiency due to the axial waveguide configuration and nanocavity function of nanowire. However, for thin nanowires, stable modes cannot be supported, resulting in very poor Purcell factor which is an important parameter of single photon sources. In this paper, a novel single photon source structure with a high Purcell factor is proposed and simulated. The structure consists of a GaAs nanowire embedded with an InAs quantum dot surrounded by Au. The enhancement of the Purcell factor is simulated by finite difference time domain (FDTD) method. Without Au shell, the Purcell factor quickly drops as the diameter of nanowire decreases. When the diameter is decreased to 50 nm, the nanowire cannot support any stable modes, resulting in a rather low Purcell factor of 0.009. After the Au shell is introduced, the Purcell factor is dramatically enhanced, and the enhancement ratio increases as the nanowire diameter decreases. The highest enhancement ratio of 1028 can be obtained at a nanowire diameter of 25 nm and Au shell thickness of 75 nm. The enhancement of the Purcell factor is attributed to the decrease of the cavity effective mode volume, which is inversely proportion to the Purcell factor. This work may offer a way to achieve single photon sources with an ultra-small size and ultrahigh Purcell factor.