<p>Conjugate gradient methods for solving vector optimization problems provide an alternative approach to scalarization techniques that do not require assigning weights to specific objective functions. This paper proposes a hybrid conjugate gradient method as a convex combination of modified Liu–Storey and Dai–Yuan conjugate gradient methods. This approach guarantees a sufficient descent property for the vector search direction and satisfies the Dai–Liao vector conjugacy condition independent of any line search. The global convergence is established using the Wolfe line search without regular restart and assuming convexity on the objective functions. We conducted numerical experiments to showcase the implementation and effectiveness of the proposed hybrid method over the Liu–Storey and Dai–Yuan conjugate gradient methods.</p>