Terahertz continuous-wave (CW) sources oscillating around the 1.0 THz band at room temperature have rapidly been developed to bridge the terahertz gap. However, reflectionless metasurfaces suitable for integration with terahertz CW sources as optical components have yet to be developed in the terahertz gap. Here, we propose a terahertz-focusing metalens consisting of reflectionless meta-atoms with a discrete distribution of negative refractive indices from ${-}{1.1}$ to ${-}{2.8}$. The proposed 2D gradient-refractive-index metalens converts an incident terahertz Gaussian beam to a line focus. We also experimentally demonstrate a metasurface of reflectionless meta-atoms with a negative refractive index of ${-}{2.8}$ adopted in the periphery of the metalens. The reflectionless metasurface in the terahertz gap would be a welcome contribution to the rapid growth of terahertz industrial applications with terahertz CW sources. Further, the design approach based on reflectionless meta-atoms with negative refractive indices could be applied to various 2D planar optical components with attractive functionalities such as collimating, arbitrary wavefront shaping, and light vortices.