An achromatic doublet lens (ADL) for surface plasmon polaritons (SPPs) is designed. Similar to the conventional ADL, the proposed plasmonic ADL is composed of two lens layers with different dispersion relations. Considering these layers as effective media, their refractive indices with respect to the free-space wavelength are calculated. Geometric parameters of the lens are initially set according to the geometrical optic theory, and then optimized by reduced dimensional calculations. The performance of proposed device is verified by using full-wave simulations and compared with a double-convex plasmonic lens to verify its achromatic characteristics. It is shown that the standard deviation of the focal length shift is reduced from 668 nm to 168 nm, after introducing the ADL.