In this paper the drivability of a parallel hybrid electric vehicle (HEV) is investigated. The standard Equivalent Consumption Minimization Strategy (ECMS) has been adapted to take into account drivability performance indexes without a posteriori corrections that lead to suboptimal solutions. It can be shown that, for this class of vehicle, a trade off between fuel economy and drivability is possible: in the case of the application considered in this paper, for example, the performance indexes of drivability can be improved by a factor 2 while the fuel consumption increases by only 1%. The solution of the reformulated optimal control problem has been developed with offline tools and then an online implementation through static maps has been derived.