This article proposes a new gamut-mapping algorithm (GMA) that utilizes both lightness mapping and multiple anchor points. The proposed lightness mapping minimizes the lightness difference of the maximum chroma between two gamuts and produces the linear tone in bright and dark regions. In the chroma mapping, a separate mapping method that utilizes multiple anchor points with constant slopes plus a fixed anchor point is proposed to maintain the maximum chroma and produce a uniform tonal dynamic range. As a result, the proposed algorithm is able to reproduce high quality images using low-cost color devices.