  In this paper we study the Schwarzschild AdS black hole with a cloud of
string background in an extended phase space and investigate a new phase
transition related to the topological charge. By treating the topological
charge as a new charge for black hole solution we study its thermodynamics in
this new extended phase space. We treat by two approaches to study the phase
transition behavior via both $T-S$ and $P-v$ criticality and we find the
results confirm each other in a nice way. It is shown a cloud of strings
affects the critical physical quantities and it could be observed an
interesting Van der Waals-like phase transition in the extended thermodynamics.
The swallow tail-like behavior is also observed in Free Energy-Temperature
diagram. We observe in $a\to 0$ limit the small/large black hole phase
transition reduces to the Hawking-Page phase transition as we expects. We can
deduce that the impact of cloud of strings in Schwarzschild black hole can
bring Van der Waals-like black hole phase transition.
