In order to study the relation between the space between layers and the resonant frequency in periodic structures left-handed materials, the prism-shaped samples are produced as the spacing of 3.08 mm, 2.93 mm, 2.73 mm and 2.33 mm. The diagrams of the intensity and frequency are obtained by measuring the refraction of electromagnetic waves through the samples with HP8720ES scalar network analyzer. And the curves of the electromagnetic wave frequency and intensity are simulated of the spacing for 3.23 mm, 3.13 mm, 3.03 mm, 2.93 mm and 2.73 mm of prism-shaped samples.Experimental and simulation results are consistent, that is, the resonant frequency shifts from high frequency to low frequency with the decreasing space between layers.