Traditional meta-surfaces generally utilize propagation phase, geometric phase or their combinations for realizing manipulating scatterings of electromagnetic (EM) waves, and are mostly in the light of normal incidence. When incident EM waves become oblique, the performance of manipulating EM waves will become worse due to impedance mismatch, especially for large incidence angles. Fortunately, detour phase provides controlling obliquely incident EM waves with an alternative method, which can be introduced by moving meta-atoms from their original periodic lattices instead of changing the structure parameters or rotating the meta-atoms. This paper proposes a design strategy of independently manipulating EM waves under different incidence angles based on the combination of detour phase and geometric phase. As a proof-of-principle, a split ring resonator (SRR) is chosen as the meta-atom, which can achieve broadband polarization conversion. The meta-surface is formed by shifting and rotating the SRR meta-atoms to simultaneously introduce detour phase and geometric phase. When EM waves are incident normally upon the meta-surface, the scattered waves are split into two beams due to the geometric phase design. While under oblique incidence, most scattered waves are funneled into the -1st diffraction order and then are deflected by the detour phase design. Both the simulated and measured results show excellent performances. This method enriches the degree of freedom to manipulate EM waves using meta-surfaces and can be extended to full-space beam engineering by further combining with propagation phase, resonance phase, etc.