ABSTRACT As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM), we present a measurement of the mass of the supermassive black hole (SMBH) in the nearby early-type galaxy NGC 0383 (radio source 3C 031). This measurement is based on Atacama Large Millimeter/sub-millimeter Array (ALMA) cycle 4 and 5 observations of the 12CO(2–1) emission line with a spatial resolution of 58 × 32 pc2 (0.18 arcsec × 0.1 arcsec). This resolution, combined with a channel width of 10 km s−1, allows us to well resolve the radius of the black hole sphere of influence (measured as RSOI = 316 pc = 0.98 arcsec), where we detect a clear Keplerian increase of the rotation velocities. NGC 0383 has a kinematically relaxed, smooth nuclear molecular gas disc with weak ring/spiral features. We forward model the ALMA data cube with the Kinematic Molecular Simulation (KinMS) tool and a Bayesian Markov Chain Monte Carlo method to measure an SMBH mass of (4.2 ± 0.7) × 109 M⊙, a F160W-band stellar mass-to-light ratio that varies from 2.8 ± 0.6 M⊙/L$_{⊙ ,\, \mathrm{F160W}}$ in the centre to 2.4 ± 0.3 M⊙$/\rm L_{⊙ ,\, \mathrm{F160W}}$ at the outer edge of the disc and a molecular gas velocity dispersion of 8.3 ± 2.1 km s−1(all 3σ uncertainties). We also detect unresolved continuum emission across the full bandwidth, consistent with synchrotron emission from an active galactic nucleus. This work demonstrates that low-J CO emission can resolve gas very close to the SMBH ($≈ 140\, 000$ Schwarzschild radii) and hence that the molecular gas method is highly complimentary to megamaser observations, as it can probe the same emitting material.