The existing secure e-auction schemes are shown to be too costly for users using mobile devices in wireless network as they heavily depend on costly asymmetric cipher. A new secure e-auction efficient enough for devices with low computation capability and limited communication bandwidth is designed in this paper. Most of its operations are symmetric cipher computations and the only asymmetric cipher operations it needs for a bidder are several multiplications. With so high efficiency, its still achieves the normal security properties of secure e-auction.