Current crowding at bends of superconducting nanowire single-photon detectors is one of the main factors limiting the performance of meander-style detectors with large filling factors. In this paper, we propose a new concept to reduce influence of the current crowding effect, a so-called variable thickness SNSPD, which is composed of two regions with different thicknesses. A larger thickness of bends in comparison to the thickness of straight nanowire sections locally reduces the current density and reduces the suppression of the critical current caused by the current crowding. This allows variable thickness SNSPD to have a higher critical current, an improved detection efficiency, and decreased dark count rate in comparison with a standard uniform thickness SNSPD with an identical geometry and film quality.