The construction phase effort prediction is needed for assigning resources to teams of practitioners destined specifically to this phase of the software development life cycle (SDLC). Construction effort (CE) has been reported between 27.5% and 58% of the total SDLC effort causing the uncertainty of taking these percentages as reference. A support vector regression (SVR) training involves quadratic programming problems that can analytically be solved using a sequential minimal optimization (SMO) algorithm. Moreover, a Pearson VII (PUK) kernel is useful to replace a set of kernel functions commonly used by a SVR. The objective of this study is to apply the SMO with the PUK to train SVR for predicting CE. The SVR model trained with the SMO algorithm having as kernel to the PUK (SVR-SMO-PUK) prediction accuracy was statistically compared to those accuracies obtained from statistical regression (SR), neural network (NN), and two types of SVR. Seven international public data sets of software projects were used. Results showed that the SVR-SMO-PUK was better than the SR in five data sets and better than NN in two of these five data sets. It was equal than SR and NN in the remaining two data sets. It was equal than ε-SVR and ʋ-SVR in the seven data sets. Thus, the SVR-SMO-PUK is useful to software managers to predict CE.