Disclosed is a shell-and-tube heat exchanger type reactor that can be used for a process of producing unsaturated acids from olefins via fixed-bed catalytic partial oxidation, which comprises at least one reaction tube, each including at least one first-step catalyst layer, in which olefins are oxidized by a first-step catalyst to mainly produce unsaturated aldehydes, and at least two second-step catalyst layers, in which the unsaturated aldehydes are oxidized by a second-step catalyst to produce unsaturated acids, wherein a first catalyst layer of the second-step catalyst layers, disposed right adjacent to the first-step catalyst layer, has an activity corresponding to 5˜30% of the activity of the catalyst layer having a highest activity among the second-step catalyst layers. A method of producing unsaturated acids from olefins by using the reactor is also disclosed.