First of all, current doesn't flow. Charge flows. The conventional direction of the current is from + to -, and this direction can be the same as the direction of actual charge flow or the opposite, depending on the type of the charge carrier. As you know, the formula of definition for the electric current is I = dq/dt.
Now, if we consider a conductor, in which the charge carrier is the electron which is a negative charge, the dq term will also be negative and so will be I in the direction of the electron flow. That's why the direction in which I will be positive is the opposite direction of actual electron flow, meaning that the electrons actually flow from - to +.
If we consider a semiconductor, in which there are two charge carriers - the electron and the hole (which is a positive charge) - the electric current will be given by the flow of both (electrons and holes). While the direction of the actual electrons flow will be from - to +, the direction of actual holes flow will be from + to - (the same as the conventional current direction) because for the hole current the dq term is positive.
So, yes, charge can flow from + to - and from - to + in the same time (for example in a PN junction) but the direction of the electric current is from + to -.