A compressive sensing (CS) approach is proposed for the complex wave retrieval algorithm from single off-axis digital Fresnel holography to improve the accuracy of quantitative phase measurement. The linear model of non-linear holographic process used in the complex wave retrieval algorithm is utilized to meet the linearity requirement of the proposed CS implementation presented in this paper. The error in object wave reconstruction due to the approximations used in complex wave retrieval algorithm is compensated by combining it with CS approach. A Mach–Zehnder interferometric geometry in transmission and off-axis mode in the Fresnel domain is used to record the digital hologram. The numerical simulations and experimental results are presented to demonstrate and validate the proof of the concept and to compare CS frame work with conventional complex wave retrieval algorithm. The proposed algorithm is tested for the microlens sample characterization by considering the parameters such as height, diameter and radius of curvature. A Haar wavelet based object wave sparsification is used in the experiment for the prudent phase reconstruction in the CS approach. The proposed method enables an improved and accurate object phase reconstruction, with minimal noise such as distortions or speckles with respect to the conventional complex wave retrieval method. © 2020 Elsevier B.V.