As part of the mm-Wave Interferometric Survey of Dark Object Masses ( WISDOM ) project we present an estimate of the mass of the supermassive black hole ( SMBH ) in the nearby fast-rotating early-type galaxy NGC4429 , that is barred and has a boxy/peanut-shaped bulge . This estimate is based on Atacama Large Millimeter/submillimeter Array ( ALMA ) cycle-2 observations of the ^ { 12 } CO ( 3–2 ) emission line with a linear resolution of \approx 13 pc ( 0 . ^ { \prime \prime } 18 \times 0 . ^ { \prime \prime } 14 ) . NGC4429 has a relaxed , flocculent nuclear disc of molecular gas that is truncated at small radii , likely due to the combined effects of gas stability and tidal shear . The warm/dense ^ { 12 } CO ( 3-2 ) emitting gas is confined to the inner parts of this disc , likely again because the gas becomes more stable at larger radii , preventing star formation . The gas disc has a low velocity dispersion of 2.2 ^ { +0.68 } _ { -0.65 } km s ^ { -1 } . Despite the inner truncation of the gas disc , we are able to model the kinematics of the gas and estimate a mass of ( 1.5 \pm 0.1 ^ { +0.15 } _ { -0.35 } ) \times 10 ^ { 8 } M _ { \odot } for the SMBH in NGC4429 ( where the quoted uncertainties reflect the random and systematic uncertainties , respectively ) , consistent with a previous upper limit set using ionised gas kinematics . We confirm that the V -band mass-to-light ratio changes by \approx 30 % within the inner 400 pc of NGC4429 , as suggested by other authors . This SMBH mass measurement based on molecular gas kinematics , the sixth presented in the literature , once again demonstrates the power of ALMA to constrain SMBH masses .