The postburst object of a GRB is likely to be a highly magnetized, rapidly rotating compact object (e.g., a millisecond magnetar), which could produce an ultrarelativistic electron-positron-pair wind. The interaction of such a wind with an outwardly expanding fireball ejected during the burst leads to a relativistic wind bubble (RWB). We numerically calculate the dynamics and radiative properties of RWBs and use this model to explain the shallow decay phase of the early X-ray afterglows observed by Swift. We find that RWBs can fall into two types: forward-shock-dominated and reverse-shock-dominated bubbles. Their radiation during a period of $∼ 10^{2}-10^{5}$ seconds is dominated by the shocked medium and the shocked wind, respectively, based on different magnetic energy fractions of the shocked materials. For both types, the resulting light curves always have a shallow decay phase. In addition, we provide an example fit to the X-ray afterglows of GRB 060813 and GRB 060814 and show that they could be produced by forward-shock-dominated and reverse-shock-dominated bubbles, respectively. This implies that, for some early afterglows (e.g., GRB 060814), the long-lasting reverse shock emission is strong enough to explain their shallow decay phase. Comment: 5 pages, 4 figures, Accepted for Publication in A&A