Using the CK direct method, we obtain the similarity reduction of coupled KdV equation, which is then explained in detail by group theory. To check the Painlev integrability of coupled KdV equation, the reduction equation is also classified by means of the Painlev test, and three types of P-integrable models are found. Finally, it is shown that the coupled KdV equation has kinds of traveling wave solutions, including conoidal periodic wave solution, soliton solution, and so on.