Effort estimation is the most critical activity for the success of overall solution delivery in software engineering projects. In this context, the paper's main contributions to the literature on software effort estimation are twofold. First, this paper examines the application of meta-heuristic algorithms to have a logical and acceptable parametric model for software effort estimation. Secondly, to unravel the benefits of nature-inspired meta-heuristic algorithms usage in optimizing Deep Learning (DL) architectures for software effort estimation, this paper presents a Deep Neural Network (DNN) model for software effort estimation based on meta-heuristic algorithms. In this paper, Grey Wolf Optimizer (GWO) and StrawBerry (SB) meta-heuristic algorithms are applied for having a logical and acceptable parametric model for software effort estimation. To validate the performances of these two algorithms, a set of nine benchmark functions having wide dimensions is applied. Results from GWO and SB algorithms are compared with five other meta-heuristic algorithms used in literature for software effort estimation. Experimental results showed that the GWO has comprehensive superiority in terms of accuracy in estimation. The proposed DNN model (GWDNNSB) using meta-heuristic algorithms for initial weights and learning rate selection, produced better results compared to existing work on using DNN for software effort estimation.