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It is known that for a microstrip antenna (patch antenna) resonant in a single mode, if the height of the antenna is strictly limited, the bandwidth is narrow, and the performance at the side frequencies is worse than that at the centre frequency. A way to solve this problem is to combine two modes into one single narrow band. However, almost all the two-mode resonance methods reported are for wideband patch antennas because the frequency ratio of two bands is commonly large and hard to decrease. In this article, a detailed mode analysis based on transmission line theory is performed, and a mode shift theory is established for patch antennas. A dual-mode patch antenna with any frequency ratio can be designed. Guided by this theory, a low-profile patch antenna with a size of only 0.23λ₀×0.23λ₀×0.027λ₀ (λ₀ is the wavelength of the centre frequency in free space) for the Beidou BD3 band (1.258 GHz-1.278 GHz) is designed. The antenna resonates in two modes, and the frequency ratio is only 1.02. The simulated and measured results show that the gain performance of the proposed antenna is almost flat over the operating band (3 dBic-3.1 dBic), which is hard to achieve through any other bandwidth enhancement method.