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Image edge detection is a fundamental problem in image processing and computer vision, particularly in the area of feature extraction. However, the time complexity increases squarely with the increase of image resolution in conventional serial computing mode. This results in being unbearably time consuming when dealing with a large amount of image data. In this paper, a novel resolution free parallel implementation algorithm for gradient based edge detection, namely EDENP, is proposed. The key point of our method is the introduction of an enzymatic numerical P system (ENPS) to design the parallel computing algorithm for image processing for the first time. The proposed algorithm is based on a cell-like P system with a nested membrane structure containing four membranes. The start and stop of the system is controlled by the variables in the skin membrane. The calculation of edge detection is performed in the inner three membranes in a parallel way. The performance and efficiency of this algorithm are evaluated on the CUDA platform. The main advantage of EDENP is that the time complexity of O (1) can be achieved regardless of image resolution theoretically. [ABSTRACT FROM AUTHOR]