By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the objective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of complete metric spaces (*Z*, *d*), we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain *X* ⊂ *Z* is countably compact in any Hausdorff topology weaker than that induced by *d*. When (*Z*, *d*) is a Féchet space (i.e., a complete metrizable locally convex space), our existence result only requires that the domain *X* ⊂ *Z* is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems, which extend and improve the related known results.