The concept of vectorial nonparaxial Hermite-cosine-Gaussian(HCosG)beams is introduced and their free space propagation equations are derived analytically by using the vectorial Rayleigh-Sommerfeld diffraction integrals and the on-axis and far-field expressions as well as paraxial propagation formula are obtained in free space. Numerical calculations and analysis show that,the f-parameter and decentered parameter play important roles in determining the nonparaxiality of vectorial HCosG beams. In addition,the on-axis intensity distribution is relative to the beam order and its parity.