This letter proposes an energy-detection-based non-data-aided weighted non-coherent receiver (NDA-WNCR) scheme for impulse radio ultra-wideband (IR-UWB) pulse-position modulated signals. Compared to the conventional WNCR, the optimal weights of the proposed NDA-WNCR are tremendously simplified as the maximum eigenvector of the IR-UWB signal energy sample autocorrelation matrix. The NDA-WNCR serves to blindly obtain the optimal weights and entirely circumvent the transmission of training symbols or channel estimation in practice. Analysis and simulation results verify that the bit error rate (BER) performance of the NDA-WNCR closely approaches the ideal BER of the conventional WNCRs.