Based on the color-singlet model, we investigate the photoproduction of J/ψ associated with a c c̅ pair with all subprocesses including the direct, single-resolved, and double-resolved channels. The amplitude squared of these subprocesses are obtained analytically. By choosing corresponding parameters, we give theoretical predictions for the J/ψ transverse momentum distributions both at the LEPII and at the future photon colliders for these subprocesses. The numerical results show that at the

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... PII these processes can not give enough contributions to account for the experimental data, and it indicates that the color-octet mechanism may still be needed. At the photon collider with the laser back scattering photons, the resolved photon channe will dominate over the direct one in small and moderate p_t regions with large √(s). By measuring the J/ψ production associated with a cc̅ pair, this process can be separated from the inclusive J/ψ production and may provide a new chance to test the color-singlet contributions.