The present study aimed to optimize the production of L-asparaginase from Aspergillus arenarioides EAN603 in submerged fermentation using a radial basis function neural network with a specific genetic algorithm (RBFNN-GA) and response surface methodology (RSM). Independent factors used included temperature (x1), pH (x2), incubation time (x3), and soybean concentration (x4). The coefficient of the predicted model using the Box–Behnken design (BBD) was R2 = 0.9079 (p < 0.05); however, the lack of fit was significant indicating that independent factors are not fitted with the quadratic model. These results were confirmed during the optimization process, which revealed that the standard error (SE) of the predicted model was 11.65 while the coefficient was 0.9799, at which 145.35 and 124.54 IU mL−1 of the actual and predicted enzyme production was recorded at 34 °C, pH 8.5, after 7 days and with 10 g L−1 of organic soybean powder concentrations. Compared to the RBFNN-GA, the results revealed that the investigated factors had benefits and effects on L-asparaginase, with a correlation coefficient of R = 0.935484, and can classify 91.666667% of the test data samples with a better degree of precision; the actual values are higher than the predicted values for the L-asparaginase data.