The Schmidl and Cox (SC) packet detector uses the ratio of the power of a received packet and the power of its own packet delayed by the periodicity of preamble. If the ratio exceeds a ratio threshold (T) with a non-zero value less than one, the SC packet detector declares that a packet is detected. However, it can make a false detection when there is a DC offset during no packet. This paper has proposed the modified SC packet detector with two limiters to increase the probability of correct packet detection even if there is a DC offset.