Crystalline silicon solar cells with $SiN_x/SiN_x$ and $SiN_x/SiO_x$ double layer anti-reflection coatings(ARC) were studied in this paper. Optimizing passivation effect and optical properties of $SiN_x$ and $SiO_x$ layer deposited by PECVD was performed prior to double layer application. When the refractive index (n) of silicon nitride was varied in range of 1.9~2.3, silicon wafer deposited with silicon nitride layer of 80 nm thickness and n= 2.2 showed the effective lifetime of $1,370{mu}m$. Silicon nitride with n= 1.9 had the smallest extinction coefficient among these conditions. Silicon oxide layer with 110 nm thickness and n= 1.46 showed the extinction coefficient spectrum near to zero in the 300~1,100 nm region, similar to silicon nitride with n= 1.9. Thus silicon nitride with n= 1.9 and silicon oxide with n= 1.46 would be proper as the upper ARC layer with low extinction coefficient, and silicon nitride with n=2.2 as the lower layer with good passivation effect. As a result, the double layer AR coated silicon wafer showed lower surface reflection and so more light absorption, compared with $SiN_x$ single layer. With the completed solar cell with $SiN_x/SiN_x$ of n= 2.2/1.9 and $SiN_x/SiO_x$ of n= 2.2/1.46, the electrical characteristics was improved as ${Delta}V_{oc}$= 3.7 mV, ${Delta}_{sc}=0.11mA/cm^2$ and ${Delta}V_{oc}$=5.2 mV, ${Delta}J_{sc}=0.23mA/cm^2$, respectively. It led to the efficiency improvement as 0.1% and 0.23%.