In this work some modifications of the iterative methods and new methods presented for solving non-linear equations. The order of convergence and corresponding error equations of our methods is derived analytically and with the help of Maple program. We noted that the convergence analysis of our methods have order of convergence three, four, five, six, seven and ten. The efficiency of the method is tested on several numerical examples. It is observed that our methods is comparable with the well-known existing methods and in many cases gives better results. Also, our methods are competing with the other iterative methods of simple roots for solving non-linear equations.