In this paper, we propose a design of dual-band patch antennas for Global Positioning System(GPS) applications, and the designed antenna is used as an individual element of GPS arrays. A low distortion and a high isolation of the array are achieved by adjusting rotating angles of each array element. The antenna consists of two radiating patches that operate in the GPS $L_1$ and $L_2$ bands, and the two ports feeding network with a hybrid chip coupler is adopted to achieve a broad circular polarization(CP) bandwidth. The rotating angles of each antenna element are varied with four directions(${phi}=0^{circ}$, ${phi}=90^{circ}$, ${phi}=180^{circ}$, ${phi}=270^{circ}$) in order to minimize the pattern distortion and maximize the isolation among array elements. The measurement shows bore-sight gains of 0.3 dBic($L_1$) and -1.0 dBic($L_2$) for the center element. Bore-sight gains of 1.6 dBic($L_1$) and 1.0 dBic($L_2$) are observed for the edge element. This results demonstrate that the proposed antenna is suitable for GPS array applications.