An endfire antenna with sum and difference beams is designed based on phase transforming of a proposed asymmetric spoof surface plasmon polariton (SSPP) structure. The asymmetric arrays of grooves, with different groove depths, periods, and/or duty ratios, serve as transmission structure and transmit electromagnetic (EM) waves in SSPP modes. Due to the distinct phase constants for the EM fields on the two sides of the asymmetric structures, the transformation of phase difference for the EM waves is realized. Superposition in the endfire direction for the in-phase and out-of-phase EM fields forms the endfire radiations with sum and difference beams. A design procedure is proposed where operating frequencies of the endfire antenna are predicted with the dispersion curves of the asymmetric SSPP structures and allocated by phase transformation. A prototype is implemented to validate the proposed design principle. Sum beam operating frequencies of the endfire antenna are at 5.50, 6.60, and 7.09 GHz, while difference beams appear at 6.10 and 6.90 GHz. Good agreement of the results validates the feasibility of the proposed mechanism and design procedure. The proposed endfire antenna with sum and difference beams has broad prospect in direction finding, tracking, and anti-interference applications.