This paper proposes a new method to design a single-layer dual-band circularly polarized (CP) patch antenna with a small frequency ratio. The design consists of one or several pairs of rectangular patches proximity-fed by a 50-Ω microstrip line with an open-circuit termination. By exploiting both capacitive and inductive coupling mechanisms, and both orthogonal radiating modes of these patches, the antenna can be designed to operate at two close resonance frequencies. Due to its simple and single-layer structure, the antenna can be easily adapted with meshed configuration, which is suitable for transparent devices. For verification, a dual-band CP meshed patch antenna with a frequency ratio of 1.12 and two pairs of patch is designed, fabricated, and tested. The measurements show that the antenna prototype provides a | <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> | < -10-dB bandwidth of 4.82–5.03 GHz (210 MHz) and 5.49–5.78 GHz (290 MHz), axial ratio < 3-dB bandwidth of 4.88–4.93 GHz (50 MHz) and 5.50–5.57 GHz (70 MHz), and broadside realized gains of 9.0 dBic and 8.6 dBic for the lower and upper bands, respectively.