This paper addresses a dynamic lot sizing problem with mixed backlogging and outsourcing and non-decreasing inventory capacity. In this problem, outsourcing can occur in a period even if the inventory level at that period is positive, and outsourcing level at each period can not exceed the demand of that period. The outsourcing, backlogging and holding costs are linear. Production cost may include setup cost, and the production capacity is unlimited. The goal is to satisfy all demands in planning horizon and minimize the total cost. Some properties of an optimal solution are introduced. Based on these properties a dynamic programming algorithm with complexity O(T4) is developed to solve this problem, where T is number of periods in planning horizon. Numeric results show that our algorithm is high performance with the length of planning horizon.