Following a key idea of unconventional geometric quantum computation developed earlier [S. L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003)], here we propose a more general scheme in such an intriguing way: {gamma}{sub d}={alpha}{sub g}+{eta}{gamma}{sub g}, where {gamma}{sub d} and {gamma}{sub g} are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with {eta} as a constant and {alpha}{sub g} being dependent only on the geometric feature of the operation. More interestingly, we demonstrate an experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.