The simultaneous ground‐state cooling (SGC) and quantum synchronization of multi‐mode mechanical resonators in the cavity optomechanical system are both attractive research domains and have been developed separately. In this paper, the influence of optical parametric amplifier on improving SGC and quantum synchronization is investigated. It is found that the nonlinear medium can suppress the Stokes heating term because of the destructive interference between the counter‐rotating term and the optical parametric amplification term, thereby improving cooling rate. More importantly, the relation between SGC and quantum synchronization is analyzed, and it is shown that SGC must be accompanied by quantum synchronization, but quantum synchronization does not require SGC. The conclusion connects the two fields and provides a well understanding of the two phenomena. [ABSTRACT FROM AUTHOR]