In this Letter, we report properties of surface plasmon resonances (SPRs) on metal gratings with periodic phase shifts, in which high-order SPR modes corresponding to the long-pitch (a few to tens of wavelengths, λ) phase shifts are excited, instead of those corresponding to the short-pitch (∼λ) gratings. In particular, it is shown that, for quarter-phase shifts, spectral features of doublet SPR modes with narrower bandwidths are notably present when the underlying first-order short-pitch SPR mode is designed to be located between an arbitrarily chosen pair of neighboring high-order long-pitch SPR modes. Also, the positions and interspacing of the doublet SPR modes can be arbitrarily tuned by adjusting the pitch values. Resonance characteristics of this phenomenon are numerically investigated, and an analytical formulation based on coupled-wave theory is developed to elucidate the resonance conditions. Characteristics of the narrower-band doublet SPR modes may find application in the resonant control of light-matter interactions involving photons of multiple frequencies, and in high-precision SPR sensing with multi-probing channels.