Metasurfaces with spin-selective transmission play an increasingly critical role in realizing optical chiral responses, especially for strong intrinsic chirality, which is limited to complex three-dimensional geometry. In this paper, we propose a planar metasurface capable of generating maximal intrinsic chirality and achieving dual-band spin-selective transmission utilizing dual quasi-bound states in the continuum (quasi-BICs) caused by the structural symmetry breaking. Interestingly, the value of circular dichroism (CD) and the transmittance of two kinds of circular polarization states can be arbitrarily controlled by tuning the asymmetry parameter. Remarkable CD approaching unity with the maximum transmittance up to 0.95 is experimentally achieved in the dual band. Furthermore, assisted by chiral BICs, the application in polarization multiplexed near-field image display is also exhibited. Our work provides a new avenue to flexibly control intrinsic chirality in planar structure and offers an alternative strategy to develop chiral sensing, multiband spin-selective transmission, and high-performance circularly polarized wave detection. The basic principle and design method of our experiments in the microwave regime can be extended to other bands, such as the terahertz and infrared wavelengths.