Whole body parametric PET imaging uses multiple dynamic frames to calculate the rate of activity change over time in each image voxel. To evaluate tracer kinetics accurately, ideally each voxel in different dynamic frames should contain the same tissue for the duration of the dynamic scan. However, patients may move voluntarily or involuntarily during dynamic data acquisition, and the corresponding shifts in tissue positions can create motion artifacts in reconstructed parametric images. Therefore, inter-frame motion correction is an important step to achieve good image quality in parametric PET. In this paper, we proposed to use symmetric and inverse consistent deformable image registration for motion correction in direct whole body parametric PET. For the dynamic datasets, we select a reference frame, then calculate forward and inverse motion fields for each other frames relative to the reference frame. The calculated motion fields were incorporated in the direct Patlak reconstruction in the nested loop to make sure the same voxel in different dynamic frames contains the same tissue in the nested parametric fitting. The proposed method was validated with patient data. The motion artifacts in parametric images were significantly reduced and the corrected parametric images were more quantitatively correct.