The invention discloses a prestressed concrete constructing process for a curved shape memory alloy tendon. The constructing process specifically comprises the following steps: a plurality of curved shape memory alloy tendons are embedded into a template along the length direction of the concrete, and two ends of each tendon are allowed to respectively penetrate through and extend out of the template; the concrete is poured in the template and integrally formed along with the curved shape memory alloy tendons; after the concrete strength reaches above 75%, the shape memory alloy tendons are in batches or gradually heated by adopting an electrothermal method, after the shape memory alloy tendons are gradually heated to appointed temperature, the shape memory alloy tendons generate the one-way shape memory effect, so that the lengths of the shape memory alloy tendons trend to be reduced to a primary memory alloy tendon shape, and the concrete generates a certain constraining force so as to generate the prestress. According to the constructing process, the crack resistance, rigidity, durability and application scope of a prestressed structure is improved, and thus the purpose of applying the prestress to the concrete can be achieved, the constructing process is simple, convenient to operate, and safe and reliable in effect.