A new method coupling the fictitious external excitation and the fundamental solution-based hybrid finite element method involving element boundary integrals only is developed for two-dimensional acoustic wave eigenvalue problems.The fictitious external excitation model of the problem over a range of frequencies exceptthe eigenvalues is firstly established,and then the solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with non-zero solutions,which are solved by the present fundamental solution-based hybrid finite elementformulation.In the present fundamental solution-based hybrid finite element,two independent element fields including the intra-element field approximated by the combination of fundamental solutions to satisfy the governing equation and the element frame field approximated by the conventional shape functions to satisfy conform between adjacent elements are linked in the modified two-variable weak variationalfunctional to produce element stiffness equation.Finally,several examples including simply and multiple connected domains are presented to demonstrate the accuracy of the present method.