From the BV images of the metal-poor globular cluster NGC 1904 obtained with the 2K CCD camera equipped on the BOAO 1.8m telescope, we construct (B - V, V) color-magnitude diagram of the cluster. The apparent V magnitudes of the RGB bump and tip have been measured from the luminosity function of the iteratively selected RGB stars in NGC 1904. Theoretical absolute $M_v$ magnitudes of the RGB bump and tip are estimated using the Yonsei-Yale isochrones. The distance modulus of NGC 1904 has been derived by comparing the observed apparent V magnitude with the estimated absolute $M_v$ magnitude of the RGB bump and tip.