Abstract: This paper used the Rayleigh expansions and impedance method to study water wave diffractions at offshore breakwater with periodic gaps. Present formulas have simple forms than previous ones. Under a normal or small incident angle, present results are the same as ones in references. When a ratio of grating constant to wavelength is larger than one, the influence of structural thickness on diffractions can be ignored, and evanescent waves play an important role. On the contrary, the effects of structural thickness on diffractions and the phenomenon of extraordinary wave transmission through the gaps are very obvious, and the role of evanescent waves gradually vanish.