In the present paper we propose two new improved iterative restoration algorithms. One is to accelerate convergence of the steepest descent method using the improved search directions, while the other accelerates convergence by using preconditioners. It is also shown that the proposed preconditioned algorithm can accelerate iteration-adaptive iterative image restoration algorithm. The preconditioner in the proposed algorithm can be implemented by using the FIR filter structure, so it can be applied to practical application with manageable amount of computation. Experimental results of the proposed methods show good perfomance improvement in the sense of both convergence speed and quality of the restored image. Although the proposed methods cannot be directly included in spatially-adaptive restoration, they can be used as pre-processing for iteration-adaptive algorithms.