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Collision of two general geodesic particles around the Kerr-Newman black hole is studied and the center-of-mass (c.m.) energy of the non-marginally and marginally bound critical particles in the direct collision and the last stable orbit collision scenarios is obtained.The constraint conditions that arbitrarily high c.m.energy can be obtained for the near-horizon collision of two general geodesic particles in the extremal Kerr-Newman black hole is found,and it is noted that the charge decreases the value of the latitude in which arbitrarily high c.m.energy can occur.