A new torsion potential function for bond rotations without rotational symmetry is proposed. This function is composed of a few Gaussian-type terms each corresponding to an eclipsed conformation of the 1,2 substituents of the C-C bonds. Different from the truncated Fourier series or the truncated cosine polynomial, it is easy to determine how many terms are needed to represent any type of torsion potential barrier at a glance using the Gaussian-type function. It could also intuitively deduce the physical meaning of the expansion parameters of the new torsion potential function, which corresponds to the barrier height, the dihedral defining the eclipsed conformations, and the size of the substituents, respectively. The new torsion potential function is also applied to the 1, 2-substituted haloethanes with satisfactory results, where three Gaussian-type terms corresponding to the fully eclipsed and the partially eclipsed conformations are needed.