Sorting is one of the fundamental problems in computer science and being used vastly in various domains. So different serial and parallel approaches have been proposed. One of the parallel sorting methods are algorithms that are based on computational model of cellular automata. A cellular automata machine is a structure of interconnected elementary automata evolving in a parallel and synchronous way .The most famous sorting algorithm for one dimensional cellular automata machine is Gordillo and Luna’s. This algorithm sorts n numbers in 2n-3 steps. In this paper three new sorting algorithms are proposed. In the two first proposed algorithms, despite using smaller neighborhood radius, sorting steps have not been changed and in the third algorithm sorting steps are reduced by regarding same neighborhood radius as Gordillo- Luna’s second algorithms.