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The undamped electron acoustic wave is a newly-observed nonlinear electrostatic plasma wave and has potential applications in ion acceleration, laser amplification and diagnostics due to its unique frequency range. We propose to make the first attempt to excite a monochromatic and stable electron acoustic wave (EAW) by two counter-propagating laser beams. The matching conditions relevant to laser frequencies, plasma density, and electron thermal velocity are derived and the harmonic effects of the EAW are excluded. Single-beam instabilities, including stimulated Raman scattering and stimulated Brillouin scattering, on the excitation process are quantified by an interaction quantity, $\eta =\gamma {\tau }_{B}$ , where γ is the growth rate of each instability and ${\tau }_{B}$ is the characteristic time of the undamped EAW. The smaller the interaction quantity, the more successfully the monochromatic and stable EAW can be excited. Using one-dimensional Vlasov–Maxwell simulations, we excite EAW wave trains which are amplitude tunable, have a duration of thousands of laser periods, and are monochromatic and stable, by carefully controlling the parameters under the above conditions.