A four-dimensional potential energy surface representing the interaction between He and hydrogen cyanide (HCN) subjected to bending vibrational motion is presented. Ab initio calculations were carried out at the coupled-cluster level with single and double excitations and a perturbative treatment of triple excitations, using a quadruple-zeta basis set and mid-bond functions. The global minimum is found in the linear He-HCN configuration with the H atom pointing towards helium at the intermolecular separation of 7.94 a0. The corresponding well depth is 30.35 cm(-1). First, the quality of the new potential has been tested by performing two comparisons with previous theoretical and experimental works. (i) The rovibrational energy levels of the He-HCN complex for a rigid linear configuration of the HCN molecule have been calculated. The dissociation energy is 8.99 cm(-1), which is slightly smaller than the semi-empirical value of 9.42 cm(-1). The transitions frequencies are found to be in good agreement with the experimental data. (ii) We performed close coupling calculations of the rotational de-excitation of rigid linear HCN in collision with He and observed a close similarity with the theoretical data published in a recent study. Second, the effects of the vibrational bending of HCN have been investigated, both for the bound levels of the He-HCN system and for the rotationally inelastic cross sections. This was performed with an approximate method using the average of the interaction potential over the vibrational bending wavefunction. While this improves slightly the comparison of calculated transitions frequencies with experiment, the cross sections remain very close to those obtained with rigid linear HCN.