Abstract: Solving loadability limit quickly is the basic requirement of online assessment for power systems voltage stability. This paper proposed a SIPSS-Lasso-BP network aiming to offline fitting and online forecasting the loadability limit. The network consisted of the similarity index of power system state（SIPSS） based screening method, the least absolute shrinkage and select operator（Lasso） algorithm and the back propagation（BP） neural network. The SIPSS based screening method screened the training samples according to their loadability limits and similarity indexes of power system state. The Lasso algorithm selected the principal system state variables which were most explanatory to the loadability limit via the modified regression analysis of the training samples. The BP network was used to offline fit and online forecast the loadability limit of the system through the cut training samples. The test results on the New England 39-bus system and a practical example show that the SIPSS-Lasso-BP network can significantly improve the efficiency of offline training the BP network and guarantee the forecasting accuracy.