Metasurfaces have exhibited versatile capacities of controlling electromagnetic (EM) waves due to the high degree of freedom of designing artificially engineered meta-atoms. For circular polarization (CP), broadband phase gradient metasurfaces (PGMs) can be realized based on P-B geometric phase by rotating meta-atoms; while for linear polarization (LP), realization of broadband phase gradients has to resort to P-B geometric phase during polarization conversion and polarization purity has to be sacrificed for broadband properties. It is still challenging to obtain broadband PGMs for LP waves without polarization conversion. In this paper, we propose the design of 2D PGMs by combining the inherently wideband geometric phases and non-resonant phases of meta-atom, under the philosophy of suppressing Lorentz resonances that usually bring about abrupt phase changes. To this end, an anisotropic meta-atom is devised which can suppress abrupt Lorentz resonances in 2D for both x- and y-polarized waves. For y-polarized waves, the central straight wire is in perpendicular to electric vector Ein of incident waves, Lorentz resonance cannot be excited although the electrical length approaches or even exceeds half a wavelength. For x-polarized waves, the central straight wire is in parallel with Ein, a split gap is opened on the center of the straight wire so as to avoid Lorentz resonance. In this way, the abrupt Lorentz resonances are suppressed in 2D and the wideband geometric phase and the gradual non-resonant phase are left for broadband PGM design. As a proof of concept, a 2D PGM prototype for LP waves was designed, fabricated and measured in microwave regime. Both simulated and measured results show that the PGM can achieve broadband beam deflection for reflected waves for both x- and y-polarized waves in broadband, without changing the LP state. This work provides a broadband route to 2D PGMs for LP waves and can be readily extended to higher frequencies such as terahertz and infrared regimes.