In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point algorithm for which we derive complexity results, thereby extending previous results by Yildirim \& Wright. Numerical results on bicriteria problems from power plant optimization and portfolio optimization show that the method is an order of magnitude faster than standard methods applied to the problems considered.