How to directly relate frictions at the level of a single molecular chain to the viscoelasticity of soft materials is intriguing. Here, we choose to investigate classical elastomers, where molecular frictions are known to be generated when dangling chains move relatively to the surrounding polymer chain network. With explicit forms employed for the relationship between friction and velocity at the molecular scale, a constitutive theory is then developed for the coupling of molecular frictions and the macroscopic viscoelasticity of elastomers. With the utilization of this theory, viscoelastic behaviors of varied elastomeric materials are predicted, which agree well with existing experiments at both low and high strain rates under different loading conditions. The theory also reproduces the time-temperature equivalent principle of elastomers. We suggest that this work might have provided a modeling framework that directly couples frictions at the level of a single molecular chain to the viscoelasticity of soft materials.