Comb-like poly(styrene-co-4-(vinylphenyl)-1-butene)-g-polyethylene copolymers (PSVS-g-PE) with various branching parameters were synthesized to study the influence of branch chains on morphology (at melt state) and linear rheological response of the copolymers. The results showed that both the branching density and branch chain length of PSVS-g-PE copolymers strongly affected linear rheological behavior of the copolymers, resulting from the formation of different microphase separation structure in the melt state. PSVS-g-PE copolymers with low branching density (2.3-3.5 branch chains per 100 repeating units of the backbone) showed a microphase-separated structure at the melt state, and a typical rheological characteristic for network-like structure was observed. Furthermore, the type of microphase-separated structure at the melt state strongly influences the applicability of the time temperature superposition (TTS) principle. As a result, the TTS failure was observed in the modulus curves for PSVS52.7-3.5-PE4.9 (poor-order lamellar structure) and PSVS54.4-2.7-PE10.7 (long tubular structure). In contrast, the PSVS-g-PE sample with high branching density (16.6-24.5 branch chains per 100 repeating units of the backbone) showed homogeneous phase structure and normal rheological behavior, similar to linear or comb-like homopolymers. The gel-like state appeared in a limited frequency regime (a plateau regime of tan delta versus omega) during decreasing the frequency from the high frequency regime in these comb-like copolymers.