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We consider a particle collision with a high center-of-mass energy near aBa\~nados-Teitelboim-Zanelli (BTZ) black hole. We obtain the center-of-massenergy of two general colliding geodesic particles in the BTZ black holespacetime. We show that the center-of-mass energy of two ingoing particles canbe arbitrarily large on an event horizon if either of the two particles has acritical angular momentum and the other has a non-critical angular momentum. Wealso show that the motion of a particle with a subcritical angular momentum isallowed near an extremal rotating BTZ black hole and that a center-of-massenergy for a tail-on collision at a point can be arbitrarily large in acritical angular momentum limit.

Particle collision with an arbitrarily high center-of-mass energy near a Ba\~nados-Teitelboim-Zanelli black hole