The frequency hopping (FH) based ultra-wideband (UWB) communication system divides its available frequency spectrum into several sub-bands, which leads to inherent disparities between carrier frequencies of each sub-band. Since the propagation loss is proportional to the square of the transmission frequency, the propagation loss on the sub-band having the highest carrier frequency is much larger than that on the sub-band having the lowest carrier frequency, resulting in disparities between received signal powers on each sub-band, which in turn leads to a bit error rate (BER) degradation in the FH UWB system. In this paper we propose an adaptive receiver for FH based UWB communications, where the integration time is adaptively adjusted relative to the hopping carrier frequency, which reduces the disparity between the received signal energies on each sub-band. Such compensation for lower received powers on sub-bands having higher carrier frequency leads to an improvement on the total average BER of the entire FH UWB communication system. We analyze the performance of the proposed reception scheme in Nakagami fading channels, and it is shown that the performance gain provided by the proposed receiver is more significant as the Nakagami fading index m increases (i.e., better channel conditions).