Polarization characteristic is an important feature of electromagnetic (EM) wave. Manipulating polarization state and controlling propagation direction of EM wave by phase-gradient metasurface (PGM) have become a research hotspot in recent years. However, using transmissive PGM for polarization manipulation often suffers a low efficiency. To alleviate this problem, multilayered structure was utilized. However, it often suffered bulky volume and design complexity. Therefore, engineering a thin high-efficiency transmissive PGM with polarization manipulation is a pressing and challenging issue. In this paper, a single-layer high-efficiency transmissive PGM with cross-polarization conversion and anomalous refraction is designed. To illustrate the working mechanism, the PGM is comprehensively investigated through theoretical analysis, EM simulations and experimental measurements. The unit cell evolving from an electric-field-coupled resonator is carefully designed to exhibit a Pancharatnam-Berry phase gradient. Each rotated element irradiated separately by the normally-incident left-handed circularly polarized (LHCP)and right-handed circularly polarized (RHCP) waves is simulated in CST microwave studio. The results show that the cross-polarization transmission magnitude keeps over 0.9 and does not change as the rotation angle varies. Moreover, the phase shift is twice the rotation angles and the direction of refracted beam is opposite under the above two different polarizations. In addition, the cross-polarization conversion ratio is above 0.9 from 14 GHz to 15.8 GHz. On the premise of high transmission magnitude, the phase of the cross-polarized transmission can be freely manipulated via varying axis orientation. By spatially arranging six unit cells in rotation angle steps of 30, a PGM with a phase difference of 60 between adjacent unit cells is designed. As is well known, linearly-polarized (LP) EM waves can be decomposed into LHCP and RHCP waves with equal amplitudes. Therefore, an LP wave through the PGM will be separated into two counterpropagating CP waves. The high-efficiency anomalous refraction of the PGM is verified from simulated near-field electric field distributions and far field normalized power patterns. The simulated refracted angle is 33.5, which is in accordance with the theoretical designed value (33.75). Moreover, the transmissive power intensity spectrum under the normally-incident LP waves is simulated and measured. The simulated and measured results are in good agreement with each other, showing that the transmitted wave is perfectly split into two counterpropagating waves from 14.9 GHz to 15.3 GHz. Compared with the available transmissive PGMs, our proposed PGM features high efficiency and thin structure with only single layer, making the proposed PGM a promising alternative to manipulating propagation and polarization of EM waves.