The prestressed shape memory alloy (SMA) strips confined columns are a novel reinforcement method, which not only exerts active confinement stress on the core concrete but also avoids the common stress hysteresis problem in reinforcement. This paper performed axial compression tests on eight sets of concrete columns with varying SMA strip width, net spacing, and pre-strain, and the impacts of these variables regarding the failure pattern, bearing capacity, and deformability of the specimens were investigated. A calculation model for the bearing capacity of SMA strips actively confined to concrete columns was established and contrasted with the prediction performance of the BP neural network. The results indicate that compared to the unconfined column, SMA strip-confined columns exhibit obvious ductile failure under compression, with the highest increase of bearing capacity and deformability reaching up to 20.27% and 24.96%, respectively. The confinement effect becomes better and better with the increasing strip width or the decreasing strip net spacing. When the strip pre-strain gradually increases, the bearing capacity of confined columns gradually improves, while the deformability first enhances and then weakens. The experimental data of other scholars is used to verify that the calculation results accord with the experimental results well, and the prediction precision of the proposed calculation model exceeds that of the BP neural network. Meanwhile, it is confirmed that the BP neural network exhibits a high fitting level in bearing capacity prediction (R2training=0.990 and R2test=0.965), offering a novel approach for predicting the bearing capacity of structures.