One of the challenges that reservoir engineers, drilling engineers, and geoscientists face in the oil and gas industry is determining the fracture density (FVDC) of reservoir rock. This critical parameter is valuable because its presence in oil and gas reservoirs boosts productivity and is pivotal for reservoir management, operation, and ultimately energy management. This valuable parameter is determined by some expensive operations such as FMI logs and core analysis techniques. As a result, this paper attempts to predict this important parameter using petrophysics logs routinely collected at oil and gas wells and by applying four robust computational algorithms and artificial intelligence hybrids. A total of 6067 data points were collected from three gas wells (#W1, #W2, and #W3) in one gas reservoir in Southwest Asia. Following feature selection, the input variables include spectral gamma ray (SGR); sonic porosity (PHIS); potassium (POTA); photoelectric absorption factor (PEF); neutron porosity (NPHI); sonic transition time (DT); bulk density (RHOB); and corrected gamma ray (CGR). In this study, four hybrids of two networks were used, including least squares support vector machine (LSSVM) and multi-layer perceptron (MLP) with two optimizers particle swarm optimizer (PSO) and genetic algorithm (GA). Four robust hybrid machine learning models were applied, and these are LSSVM-PSO/GA and MLP-PSO/GA, which had not previously used for prediction of FVDC. In addition, the k-fold cross validation method with k equal to 8 was used in this article. When the performance accuracy of the hybrid algorithms for the FVDC prediction is compared, the revealed result is LSSVM-PSO > LSSVM-GA > MLP-PSO > MLP-GA. The study revealed that the best algorithm for predicting FVDC among the four algorithms is LSSVM-PSO (for total dataset RMSE = 0.0463 1/m; R2 = 0.9995). This algorithm has several advantages, including: 1) lower adjustment parameters, 2) high search efficiency, 3) fast convergence speed, 4) increased global search capability, and 5) preventing the local optimum from falling. When compared to other models, this model has the lowest error.