There are often some efficiency losses between user equilibrium (UE) and system optimization (SO). This paper investigates the efficiency losses of multiclass stochastic user equilibrium (SUE) traffic assignment under congestioin pricing against SO. Serveral bounds of the efficiency loss for this problem when the tolls are considered as part of the system cost are derived, with the time-based criterion and the monetary-based criterion, respectively. It is shown that the upper bound of efficiency loss caused by the time-based SUE depends on the type of link travel time function, the network complexity, the travel demand, and the degree of users’ perception error on travel cost. The upper bound of efficiency loss caused by the monetary-based SUE depends on the value of time (VOT) of user classes besides the aforementioned factors.