We have undertaken a new ground-based monitoring campaign to improve the estimates of the mass of the central black hole in NGC 4151. We measure the lag time of the broad Hβ line response compared to the optical continuum at 5100 Å and find a lag of 6.6_-0.8^+1.1 days. We combine our data with the recent reanalysis of UV emission lines by Metzroth and coworkers to calculate a weighted mean of the black hole mass, M_BH = (4.57_-0.47^+0.57) × 10⁷ M _⊙. The absolute calibration of the black hole mass is based on normalization of the AGN black hole mass-stellar velocity dispersion (M _BH-σ*) relationship to that of quiescent galaxies by Onken and coworkers. The scatter in the M_BH-σ* relationship suggests that reverberation-mapping-based mass measurements are typically uncertain by a factor of 3-4.