Polymers bearing associative groups can exhibit fascinating rheological behaviors. A modified version of the Rouse model, which is originally used in block copolymers and called the sticky Rouse model here, is proposed to describe the linear viscoelasticity (LVE) of this kind of polymers without the effect of entanglement. By replacing the lifetime of a transient bond by the effective friction on stickers, the calculation of LVE functions is turned into the eigenvalue problem of the sticky Rouse-Zimm (RZ) matrix. The results show that only two parameters, sticker concentration representing the network microstructure and association interaction strength, can understand the LVE for associative polymers. In particular, the description of LVE from previous theories can be integrated in this unified theoretical framework. From the analysis of eigenvectors, it is further inferred that the rotational motion of bridge structures should be responsible for the longest relaxation times in rheology.