Millimeter wave wireless power transfer (WPT) has attracted an upsurge of interest recently. Here we present the design of a novel WPT system consisting of a wideband circularly polarized leaky wave antenna transmitter and wideband circularly polarized rectenna receiver, over the frequency band of 24–35 GHz (fractional bandwidth: 37.3%). Due to the simultaneous dual-CP radiation of the leaky-wave antenna, the proposed system overcomes the polarization misalignment issue of the antennas in the far field, thereby enabling a robust WPT. Our rectenna also realizes state-of-the-art performance in terms of bandwidth, RF-DC efficiency, and CP radiation. This is the first mmWave CP WPT system and will be experimentally verified.