Bias current dependence of a superconducting strip photon detector is studied in the wavelength range of 405 to 1310 nm. The detector is made of an $MgB_2$ meander pattern with the line width of 135 nm and thickness of 10 nm. At 1310 nm, the detection efficiency exponentially decreases as the bias current decreases. While at 405 nm, the detection efficiency almost saturates in the high bias current region. These features suggest that the intrinsic detection efficiency of the $MgB_2$ detector is high at 405 nm.