Tubing is the pipeline that transports crude oil and natural gas from the oil and gas layer to the surface of the earth. Due to the harsh operating environment, the tubing will suffer from etch pits, scratches, cracks, perforations, and even direct fractures of different degrees of defective conditions. If tubing defects are not detected and quantified in a timely manner, the continued use of tubing will result in tubing leakage and failure. Magnetic flux leakage (MFL) testing as a nondestructive testing method enables the identification and quantitative analysis of defects in metal tubing. To improve the quantification accuracy of defects in the wellhead MFL testing of tubing defects during workover operations, this paper proposes a multi-output least-squares support vector regression machine (MLSSVR) model optimized based on the simulated annealing algorithm. The size of tubing defects can be quantified by establishing the mapping between the characteristic quantity of MFL signals and the defect size. The experimental results of MFL testing of tubing defects show that the root mean square error (RMSE) of the diameter of tubing defects of the simulated annealing algorithm optimized multi-output least-squares support vector regression (SA-MLSSVR) machine model proposed in this paper is 0.4562 mm, and the RMSE of the depth of tubing defects is 0.1504 mm. Compared with the non-optimized MLSSVR model, the overall RMSE of tubing defects is reduced by 36.48%. The SA-MLSSVR model only needs one-ninth of the time to achieve the same quantification accuracy as the particle swarm optimized multi-output least-squares support vector regression machine model.