In one embodiment, a medical image processing apparatus includes a display and processing circuitry. The processing circuitry is configured to (a) calculate fluid information including flow-velocity vectors based on three-dimensional image data of plural time phases, which are acquired by a phase contrast method of magnetic resonance imaging, and in which fluid flowing inside a lumen is depicted, (b) identify a branching position where a second lumen branches from a first lumen, based on change in flow volume of fluid flowing inside the first lumen along an extending direction of the first lumen, and (c) cause the display to display an analysis result including fluid information of fluid flowing inside the second lumen, based on the branching position.
