A leaky-Vivaldi antenna covered with metasurface (LVAM) is proposed in this paper. The traditional Vivaldi antenna covered with metasurface realizes backward frequency beam-scanning from -41∘ to 0∘ in the high-frequency operating band (HFOB) and retains aperture radiation in the low-frequency operating band (LFOB). In the LFOB, the metasurface can be regarded as a transmission line to realize a slow-wave transmission. In the HFOB, the metasurface can be considered a 2D periodic leaky-wave structure to realize a fast-wave transmission. The simulated results show that LVAM has the -10 dB return loss bandwidths of 46.5% and 40.0%, and the realized gain of 8.8-9.6 dBi and 11.8-15.2 dBi cover the 5 G Sub-6 GHz band (3.3-5.3 GHz) and the X band (8.0-12.0 GHz), respectively. The test results are in good agreement with the simulated results. As a dual-band antenna covering the 5 G Sub-6 GHz communication band and military radar band, the proposed antenna can guide the future integrated design of communication and radar antenna systems.