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In this paper, we define a generalized C-condition and prove a fixed point theorem for weak (ψ, β)-contraction in partially ordered metric spaces. Our result extends the result of Suzuki [Proc. of the 8th Int. Conf. of Fixed Point Theory and Its Appl. 2007; 65: 751 — 761.] and Gupta and Mani [Functional Analysis: Theory, Methods and Applications. 2017; 3: 26 — 34]. As an application, existence and uniqueness of solution of first order periodic boundary value problem has been given in support of our finding.