As a 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-rotator early-type galaxy NGC 3665. We obtained Combined Array for Research in Millimeter Astronomy (CARMA) B and C array observations of the $^{12}$CO$(J=2-1)$ emission line with a combined angular resolution of $0.59$. We analysed and modelled the three-dimensional molecular gas kinematics, obtaining a best-fit SMBH mass $M_{rm BH}=5.75^{+1.49}_{-1.18} times 10^{8}$ $M_{odot}$, a mass-to-light ratio at $H$-band $(M/L)_{H}=1.45pm0.04$ $(M/L)_{odot, H}$, and other parameters describing the geometry of the molecular gas disc (statistical errors, all at $3sigma$ confidence). We estimate the systematic uncertainties on the stellar $M/L$ to be $approx0.2$ $(M/L)_{odot, H}$, and on the SMBH mass to be $approx0.4times10^{8}$ $M_{odot}$. The measured SMBH mass is consistent with that estimated from the latest correlations with galaxy properties. Following our older works, we also analysed and modelled the kinematics using only the major-axis position-velocity diagram, and conclude that the two methods are consistent.
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