  In this paper we consider the warped AdS$_{3}$ black hole solution of
topologically massive gravity with a negative cosmological constant, and we
investigate the possibility that it acts as a particle accelerator by analyzing
the energy in the center of mass (CM) frame of two colliding particles in the
vicinity of its horizon, which is known as the Ba\~nados, Silk and West (BSW)
process. Mainly, we show that the critical angular momentum $(L_c)$ of the
particle decreases when the parameter that controls the stretching deformation
($\nu$) increases. Also, we show that despite the particle with $L_c$ can exist
for certain values of the conserved energy outside the horizon, it will never
reach the event horizon; therefore, the black hole can not act as a particle
accelerator with arbitrarily high CM energy on the event horizon. However, such
particle could also exist inside the outer horizon being the BSW process
possible on the inner horizon. On the other hand, for the extremal warped
AdS$_{3}$ black hole, the particle with $L_c$ and energy $E$ could exist
outside the event horizon and the CM energy blows up on the event horizon if
its conserved energy fulfill the condition
$E^{2}>\frac{(\nu^{2}+3)l^{2}}{3(\nu^{2}-1)}$, being the BSW process possible.
