In this paper, a low profile, dual-band dual-polarized patch antenna is proposed for antenna-filter function with a relatively low profile of 0.032 wavelength. A simple symmetric open/short-circuited stub (O/SCS) is proposed to excite a square radiating patch, and an additional resonant mode is generated except for the patch-mode. At the lower band, the proposed antenna works as a dual-polarized patch antenna. At the upper band, transmission characteristic is obtained between the two ports, and the antenna structure can be used as a bandpass filter. A <inline-formula> <tex-math notation="LaTeX">$1\times 2$ </tex-math></inline-formula> array is also designed to validate its application potential in MIMO system. The two antennas can operate as radiators with high port isolation levels at the lower band. Meanwhile, at the upper band, the two antenna elements can act as one bandpass filter as the good transmission characteristic. In addition, a <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> array is also developed meet dual-function demands in dual-polarized MIMO systems. The low profile, simple structures and excellent performances indicate that the proposed antenna can be a good candidate in future wireless communication applications with shared functions.