The multi-tube heat exchanger includes a bundle of tubes which form fluid passages of first heat exchanging fluid, an outer shell which covers the bundle of tubes and form a fluid passage of second heat exchanging fluid, and a baffle plate which is arranged inside the outer shell in a direction intersecting an axial direction of the bundle of tubes and provided with a plurality of through holes through which respective tubes of the bundle are passed. Each of the through holes has such a shape that a portion of an outer peripheral face of the tube comes into contact with a portion of an inner peripheral face of the through hole, and a gap for passing the second heat exchanging fluid is formed between the other portion of the inner peripheral face and the outer peripheral face of the tube. It is possible to support the tubes with high dimensional accuracy, and to enhance heat exchanging efficiency by decreasing fluid resistance. It is also possible to make pitch of the through holes smaller and to make the heat exchanger compact.