Bound states can be supported on the surface of a periodically corrugated perfect conductor known as spoof surface plasmon polaritons with their dispersion curves reside below the light line.Here we show that bound states in the continuum(BICs) can also be achieved in such systems.Two types of grating structures are proposed to suppress the radiation leakage and hence generate bound states.The first one is a simple grating with broad grooves in which multiple cavity modes are accommodated.Due to the symmetry incompatibility and the destructive interaction mainly from the TM0 and TM1 modes,BICs at the Γ point and at off-Γ points are both realized.The second one is a dimerized grating with two grooves in each unit cell.The destructive interaction between the modes in the two grooves can suppresses the radiation and BICs at theΓ point are observed.The Q factors of the whole bands can be further tuned by the dimerization strength effectively.This work may offer new opportunity for the applications of metallic grating in the low frequency bands.