The formulae for average velocity of groundwater flow in a single fracture were derived based on the characteristics of fracture properties and hydraulic methods. The results show that the average velocity is proportional to the square root of the hydraulic gradient. In order to verify the results, a laboratory model was established, and the experimental data were analyzed. Experimental results indicate that the relation between the average velocity and hydraulic gradient is nonlinear, and can be fitted with power functions. And for both the unconfined and confined flows, the value of the exponent of power functions are close to 0.5. Thus the experimental results agree well with those from the theoretical analysis. By comparing the calculated and measured values of the average velocity under the same conditions, the formulae presented herein are more effective than the traditional formula based on Darcy’s Law. These results provide the evidences of non-Darcy’s flow in single fracture.