In this article, the concept of the single-objective sequential quadratically constrained quadratic programming method is extended to the multiobjective case and a new line search technique is developed for nonlinear multiobjective optimization problems. The proposed method ensures global convergence as well as spreading of the Pareto front. A descent direction is obtained by solving a quadratically constrained quadratic programming subproblem. A nondifferentiable penalty function is used to restrict the constraint violations. Convergence of the descent sequence is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. In addition to this, a new technique is designed for selecting initial points to ensure the spreading of the Pareto front. The method is compared with existing methods using a set of test problems. © 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.