The interaction potential of a He-BH complex is investigated by the coupled-cluster single-double plus perturbative triples (CCSD (T)) method and an augmented correlation consistent polarized valence (aug-cc-pV)5Z basis set extended with a set of (3s3p2d1f1g) midbond functions. Using the five two-dimensional model potentials, the first threedimensional interaction potential energy surface is constructed by interpolating along (r-re) by using a fourth-order polynomial. The cross sections for the rovibrational relaxation of BH in cold and ultracold collisions with 3 He atom are calculated based on the three-dimensional potential. The results show that the ∆v = −1 transition is more efficient than the ∆v = −2 transition, and that the process of relaxation takes place mainly between rotational energy levels with the same vibration state and the ∆j = −1 transition is the most efficient. The zero temperature quenching rate coefficient is finite as predicted by Wigner's law. The resonance is found to take place around 0.1-1 cm −1 translational energy, which gives rise to a step in the rate coefficients for temperatures around 0.1-1 K. The final rotational distributions in the state v = 0 resulting from the quenching of state (v = 1, j = 0) at three energies corresponding to the three different regimes are also given.