The purpose of this paper is to study the existence and approximation of a common fixed point of a pair of mappings satisfying a relaxed (ψ, ϕ)-weakly N-contractive condition and existence and approximation of a fixed point of a relaxed (ψ, ϕ)-weakly N-contraction mapping in the setting of modular spaces. Our theorems improve and generalize the results in Mongkolkeha and Kumam [23] and Öztürk et. al [26]. To validate our results numerical examples are provided.