Under the background of new economic normal, medium- and long- term load forecasting of power systems faces many new problems. For example, the factors affecting the power load such as GDP and population are “S”-shaped curve growth, the uncertainty between power load and power load influencing factors increases, and the number of historical samples is small. To this end, a medium- and long- term load forecasting model based on Verhulst-SVM is proposed. Firstly, the main factors affecting the electric load are extracted from the new economic normal characteristics, and the development trend of each influencing factor is analyzed. Then, the Verhulst model is used to predict the load influencing factors of the "S" curve growth. And the support vector machine (SVM) is used to replace the linear regression prediction model to achieve high-precision prediction of medium and long-term load under small sample and high uncertainty. Finally, by predicting the power load of Tianjin in 2015 and 2016, it is proved that the proposed model has high precision and reliability, which can provide reference for medium and long term power load forecasting under the background of new normal economy.