The Fused Filament Fabrication (FFF) process comprises a large number of process parameters that affect the resultant mechanical properties of the parts, generating uncertainties during the Design for Additive Manufacturing (DfAM) practice. Several studies have used Artificial Neural Networks (ANN) based on classification machine learning techniques such as Backpropagation Neural Network (BPNN), to evaluate the dimensional accuracy, surface roughness, compressive, flexural and tensile strength of FFF parts. As an alternative, in this paper a new General Regression Neural Network (GRNN) approach, based on a regression machine learning technique, is proposed to estimate the tensile structural properties of polylactic acid (PLA)-FFF parts using variable process parameters. The performance of the new proposed GRNN is compared with the performance of a BPNN. The comparison and evaluation are based on their capability to accurately predict the experimental Ultimate Tensile Stress (UTS) and the Elastic Modulus ( E) of FFF parts. The outcomes of this evaluation have shown that although the GRNN and the BPNN are able to estimate with high accuracy the structural behaviour of FFF parts, the performance of the proposed GRNN is superior (0.001 Mean Square Error, MSE) than the BPNN (0.0031 MSE). Moreover, the new proposed GRNN fits the experimental test values with a minimal average error of 0.62%. Thus, the proposed GRNN can be used during the design of components intended to be manufacture by FFF.