We propose a new kind of optical vortex called the Hermite–Gaussian-like optical vortex (HGOV) inspired by the cross phase (CP). Theoretically, we investigate how the CP is decoupled from the phase of a cylindrical lens. We also investigate the propagation characteristics of an HGOV, which has a Hermite–Gaussian-like intensity distribution but still retains the orbital angular momentum. Furthermore, we derive the Fresnel diffraction integral of an HGOV and study the purity at infinity. Besides, we show a novel function of the self-measurement of the HGOV. Finally, we show that we can change the relative positions of singularities and the direction of an HGOV precisely, which facilitates applications in optical micro-manipulation.