Non-coherent receivers are attractive for pulsed Ultra-WideBand (UWB) systems due to the implementation simplicity. However, they have to face the shortage of performance degradation. Several techniques were proposed to alleviate the noise effect and promote the receiver performance, among which is the weighted combining of multiple integration sub-intervals. In this paper, the performance of the weighted non-coherent receiver for UWB On-Off Keying (UWB-OOK) signal in multipath channels is analyzed, in terms of bit-error-rate. In addition, a closed-form expression of the approximately near-optimal weighting coefficient set is derived, and two simple weighting coefficient sets are proposed as well. Finally, the analytic results are verified via the computer simulations, which reveal obvious performance improvements to the conventional energy detector.