We present the design of a plasmonic lens (PL) which is composed of pixelated nano-grooves on a gold film for the coupling and focusing of surface plasmon polaritons (SPPs) into multiple focal spots on the optical axis. The pixelated grooves are arranged along the y-axis and the x-position of each groove is optimized by the simulated annealing algorithm. PLs that implement two and three on-axis foci are presented and the designed structures have been validated with FDTD simulations. We also successfully constructed a long-focal-depth PL with a longitudinal FWHM of the focus that reached 25 plasmonic wavelengths, while its transverse field profile is maintained over 15 µm distance. The presented design method constitutes a new basis for plasmonic beam engineering, and the proposed particular SPP focal fields have potential applications in multiple imaging, particle manipulating, and plasmonic on-chip signal transmission.