China's economy has entered a period of new normal. Meanwhile, the State Council of China issued No. 10 National Notice, which means the environment that the insurance industry faces is undergoing enormous changes. The insurance asset management has reached a new era. In that context, it is becoming more and more important for the insurance companies to choose the proper model of asset and liability management. The insurance company can only achieve its strategic objectives by making the most suitable choices to prevent and control the risks. This paper is divided into four parts. By adopting the methodology of combining document research, empirical research, model construction, induction and deduction together, we show that a combination of asset-oriented and liability-oriented asset and liability management model is expected to have a broader range of applications under the new normal. First, the paper systematically reviews the theoretical documents and summarizes the methods about asset and liability management. We point out that the insurance company should have a dynamic simulation and scientific management of its whole balance sheet through an integrative application of multiple approaches. Second, this paper compares the asset-oriented and liability-oriented asset and liability management models, based on the deep analysis on the asset and liability management model of traditional insurance companies. We argue that both models have embodied the thought of asset and liability match. They are suitable for different economic conditions and it is hard to tell which is better. When making the strategic choice, insurance companies should take various factors into account, such as the macro-environment, the company's scale and market shares, the development goals and so on. Then the paper explores and summarizes the valuable experience and inspiration of the foreign insurance companies. There is a difference in the development stage of the insurance industry home and abroad, so the foreign successful asset and liability management models do not necessarily apply in China. We should carefully analysis their successful experiences and improve the efficiency of insurance funds. At the same time, however, we must also clearly understand the differences. By analysis and comparison, we conclude that under the condition of imperfect insurance market and financial market, it is more proper for the insurance companies to apply a combination of asset-oriented and liability-oriented asset and liability management model. Under the new normal, Chinese insurance companies should prevent the mismatch of asset and liability, strengthen the portfolio management and meet the demand when designing the products and developing business. Since China's insurance industry is on its characteristic way, the insurance companies are supposed to learn from the international experience and strive for innovation and steady development.