Recently, 1H 0323+342 has attracted a lot of attention as one of several narrow-line Seyfert 1 galaxies detected in the gamma-ray band. To understand their central energy engines and jet phenomena, the black hole mass is important. We made use of the Lijiang 2.4 m Telescope to monitor 1H 0323+342 for more than two months. This galaxy is one of the candidates for a monitoring project of super-Eddington accreting massive black holes. The reverberation mapping shows that H beta emission has a delayed response of 14.8(-2.7)(+3.9) days with respect to the SDSS g' light curve in the rest frame. The optical Fe II variations were detected after subtracting host contaminations, and a reverberation with a delay of 15.2(-4.1)(+7.4) days was found in the rest frame. By assuming the viral factor f(BLR) = 6.17 for the broadline region (BLR) velocity characterized by FWHM because of the face-on orientation, we find that the black hole mass derived from H beta is M-center dot = 3.4(-0.6)(+0.9) x 10(7)M(circle dot), and the accretion rate is (M) over dot = 1.11(-0.47)(+0.69), where (M) over dot = (M) over dot(center dot)c(2)/L-Edd, (M) over dot(center dot) is the mass accretion rate, L-Edd is the Eddington luminosity, and c is the speed of light. This black hole is one order less massive than that given by the Magorrian relation from the bulge mass. We test the relation between accretion rates and radio-loudnesses in all mapped radio-loud active galactic nuclei, and find that 1H 0323+342 falls within this group.