In order to increase the signal-to-noise ratio and sensitivity of surface plasmon resonance (SPR) sensor, incident light should be coupled with surface plasmon polariton (SPP) as much as possible. The profile of a metal grating is studied in order to realize the highest SPR coupling efficient. The parameters of one-dimensional rectangular grating are optimized to find the highest SPR coupling efficient. Fourier expansion of the grating shape is used to analyze the contribution of each order to the excitation of SPR, which will provide analytic support to seek essence of physics of the max-coupling of SPR.