The recently developed state-selective (SS) multi-reference coupled-cluster (CC) method involving all singly and doubly, and semi-internal triply excited clusters from the formal reference configuration [SSCCSD(T) approach] is tested in the calculation of the potential energy surface (PES) of the HF molecule. Both double zeta and double zeta plus polarization basis sets are employed and a few different choices of active space are considered. The SSCCSD(T) method provides an accurate description of the entire RES at low cost even for the bond breaking region, contrary to the results obtained with the perturbative single-reference CCSD(T) method or various limited configuration interaction approaches. This is the first application of the new SSCC code, which uses an improved computational strategy for handling the semi-internal triexcited clusters. Details of this new implementation of the SSCCSD(T) method are discussed.