To accelerate the convergence of Kaczmarz algorithm (KA) in consistent case, an improved Kaczmarz algorithm with projection adjustment (KAPA) has been designed by the author. In order to deal with inconsistent case, extended KAPA (EKAPA) and its randomized version (ERKAPA) have been proposed in this paper. Numerical simulations of solving inconsistent linear equations have been conducted. The efficiency of EKAPA and ERKAPA have been verified by the simulation results.