A new concept called R-L model error is proposed， which can describe the accuracy of the R-L model. Simulation results show that there is a definite relationship between R-L model error and measure reactance error. The inverse-time characteristic used in distance protection based on differential equation algorithm has some defects such as conservative protection range and long time delay when the fault is at the end of the protection line. An adaptive distance protection scheme based on R-L model error is proposed to overcome the defects mentioned above. When fault occurs， zone I distance relay calculates the R-L model error in real-time and then modifies the calculation result of measure reactance adaptively according to the relationship between R-L model error and measure reactance error. Simulation results show that this new distance protection scheme can prevent transient overreach and operate rapidly even the fault is at the end of the protection line. The whole performance is enhanced greatly compared with inverse-time characteristic adopted distance protection scheme.