In this paper, the stretching vibrational spectra of some AB4 tetrahedral molecules are reported on up to the first overtone by using a one-dimensional algebraic model for the first time. The model Hamiltonian is constructed using Casimir and Majorana operators, which seems to describe the A-B stretching modes accurately using a relatively smaller number of well-defined parameters. This analysis gives a general approach for studying the vibrational spectra of any tetrahedral molecules with smaller standard deviations from the experimental results.