The development of low-k materials is essential for modern semiconductor processes to reduce the cross-talk, signal delay and capacitance between multiple layers. The effect of the $CH_4$ concentration on the formation of SiOC(-H) films and their dielectric characteristics were investigated. SiOC(-H) thin films were deposited on Si(100)/$SiO_2$/Ti/Pt substrates by plasma-enhanced chemical vapor deposition (PECVD) with $SiH_4$, $CO_2$ and $CH_4$ gas mixtures. After the deposition, the SiOC(-H) thin films were annealed in an Ar atmosphere using rapid thermal annealing (RTA) for 30min. The electrical properties of the SiOC(-H) films were then measured using an impedance analyzer. The dielectric constant decreased as the $CH_4$ concentration of low-k SiOC(-H) thin film increased. The decrease in the dielectric constant was explained in terms of the decrease of the ionic polarization due to the increase of the relative carbon content. The spectrum via Fourier transform infrared (FT-IR) spectroscopy showed a variety of bonding configurations, including Si-O-Si, H-Si-O, Si-$(CH_3)_2$, Si-$CH_3$ and $CH_x$ in the absorbance mode over the range from 650 to $4000;cm^{-1}$. The results showed that dielectric properties with different $CH_4$ concentrations are closely related to the (Si-$CH_3$)/[(Si-$CH_3$)+(Si-O)] ratio.