Spoof surface plasmon polaritons (SSPPs), analogy to surface plasmon polaritons (SPPs) in optical regime, are a hybrid electromagnetic (EM) oscillated mode of free electrons on metal surface and free space EM waves in microwave regime, which are usually excited using decorated dielectric. Determined by feeding manners, such as plane wave illuminating, coplanar waveguide (CPW) feeding, and coupling feed, the SSPPs enable even- or odd-mode. Even-mode SSPPs can form standing wave on the finite-length SSPPs guiding structure, causing broadside radiation, and odd-mode SSPPs form travelling wave, leading to endfire radiation. Based on this, in this paper, we propose a method of designing dual-band multi-beam antennas via engineering SSPPs mode. The antenna consists of several shared-aperture antennas around a common reflector and a metal ground. The shared-aperture antenna is composed of finite-length SSPPs structure and a feed monopole, achieving tri-band broadside, titled and endfire radiation, respectively, via engineering SSPPs mode. Then, through optimizing geometric configuration, the multi-beam antenna can realize dual-band multi-beam radiation patterns in azimuth. Number of the multi-beam antenna is determined by that of the single shared-aperture antenna. As an example, we designed a four-beam dual-band antenna. Simulation results verify our design. Without using complex feeding network, the proposed antenna enables dual-band multiple beams radiation, promising great potentials in compact, miniaturized, and multi-functional communication wireless system.