A modified Quadratic Partial Least Squares (MQPLS) algorithm based on nonlinear constrained programming was proposed. Sequential Unconstrained Minimization Technique (SUMT) was employed to calculate the outer input weights and the parameters of inner relationship. Other existing QPLS algorithms were also reviewed and compared with MQPLS in the applications to two data sets: one was a highly nonlinear mathematical function ever used by G. Baffi, E. B. Martin and A. J. Morris; the other was data from an industrial FCCU main fractionator. The latter was gathered to establish a soft sensor to estimate the solidifying point of diesel oil in real time. It is found that models by MQPLS have improved modeling and predictive ability, and MQPLS can avoid the problem of the pseudo-inverse of matrix and reduce the calculation burden.