The energy injection model is usually proposed to interpret the shallow-decay phase in Swift GRB X-ray afterglows. However, very few GRBs have simultaneous signatures of energy injection in their optical and X-ray afterglows. Here, we report optical
observations of GRB 090529A from 2000 sec to $sim10^6$ sec after the burst, in which an achromatic decay is seen at both wavelengths. The optical light curve shows a decay from 0.37 to 0.99 with a break at $sim10^5$ sec. In the same time interval, the decay indices of the X-ray light curve changed from 0.04 to 1.2. Comparing these values with the closure relations, the segment after 3$times10^{4}$ sec is consistent with the prediction of the forward shock in an ISM medium without any energy injection. The shallow-decay phase between 2000 to 3$times10^{4}$ sec could be due to the external shock in a wind-type-like medium with an energy injection under the condition of $ u_o < u_c < u_x$. However, the constraint of the spectral region is not well consistent with the multi-band observations. For this shallow-decay phase, other models are also possible, such as energy injection with evolving microphysical parameters, or a jet viewed off-axis,etc.
