Abstract: This paper presents a novel quantum approximate optimization algorithm to address the pervasive integer constraint problem in portfolio optimization within the financial domain. By encoding the continuous solution obtained from classical algorithms into the initial state of a quantum circuit, the algorithm transforms the continuous optimization problem into a discrete Markowitz model. Additionally, hard constraints are introduced to strictly enforce the integer constraints in the portfolio, guaranteeing solution quality. The success rate of the algorithm is further improved by using a warm starting technique. Numerical experiments demonstrate that this algorithm offers significant computational efficiency advantages and a higher solution quality compared to traditional methods when solving large-scale integer-constrained portfolio optimization problems.