Wireless power beaming (WPB) is one of the pioneering technologies for far-field wireless power transfer due to its capability to transmit power at a longer distance with increased efficiency. Impulse radio ultrawideband (IR-UWB) signals can transmit power over a wider frequency spectrum by using carrier modulated impulses with a high peak-to-average-power-ratio (PAPR). This paper presents an IR-UWB signalbased WPB system using a novel $4 \times 4$ antipodal Vivaldi antenna (AVA) array as the transmitter (TX) and receiver (RX). The designed $4 \times 4$ AVA array which has a dimension of $3 \lambda \times 1.34 \lambda$ ($\lambda$ calculated for 4 GHz), achieves a $3.4-8.4 \mathrm{GHz}$ ultrawide bandwidth (UWB), $\mathbf{1 6. 6} \mathbf{~ d B i}$ gain at $\mathbf{4} \mathbf{~ G H z}$, and a unidirectional radiation pattern, which makes it suitable for IR-UWB signalbased WPB application. This paper also presents the experimental setup of the WPB system, where the TX and RX antennas are placed 2 m apart in the far-field. An IR-UWB TX signal wavefrom is simulated and generated using the experimental setup, which has a -10 dB spectrum bandwidth of $3.7-4.3 \mathrm{GHz}$ and a total spectrum power of 34.83 dBm. A continuous wave (CW) signal of the similar total spectrum power is also generated, and the received powers for both the IR-UWB and CW signals for the WPB system are analyzed. Based on the measured received signal of the proposed WPB system, the IR-UWB signal-based WPB achieves $\mathbf{3. 7 3 \%}$ RF-RF efficiency, which is $2.27 \times$ higher than the efficiency achieved by CW signal-based WPB system.