Momentum is defined as product of mass and velocity of a body. Mass of a body is a scalar quantity but velocity is a vector quantity. Momentum being the product of a scalar quantity and a vector quantity, it is also a vector quantity.
Momentum has both magnitude and direction. Momentum of a body is a constant multiple (mass) of its velocity. Thus, momentum points in the direction of velocity.
Write the vectorial formula for momentum as shown.

Draw the figure of a body of mass m, moving with velocity  and having momentum  as shown.

Consider a body of mass m, moving with velocity  in x-direction.
Apply Newton’s second law of motion on the body.

Here, acceleration of the body is 
Rate of change of velocity is acceleration.

The equation clearly determines that direction of momentum is in x-direction because the direction of change of velocity is in x-direction.
Therefore, momentum is a vector and its direction of the momentum vector is the same as the direction of the velocity vector.