•To have consistent results an average surface Sa was selected and measured as a target.•Artificial neural network was used as an accurate tool for characterizing the interaction and effect of parameters on the surface of SLM parts.•The effect of SLM process parameters and heat treatment on the values of average surface were modeled accurately. In this paper, we propose a model to predict the average surface roughness (Sa) and analyse the effect of related process parameters on laser powder bed fusion (LPBF) selective laser melting (SLM) of Ti-6Al-4 V. The additive manufacturing (AM) process has various independent parameters that affect the quality of the produced parts and is complex to analyse. Although the process parameters can be selected separately in LPBF, they do however affect each other. Therefore, large adjustments of process parameters is not possible due to the negative effect they have on each other which can lead to problems such as cracks, balling, unmelted powders, porosity, and distortion. A range of process parameters using Taguchi L25 design of experiment (DOE) with five repetitions for each sample has been selected. Then, an artificial neural network (ANN) is applied to the model to predict the value of (arithmetical mean height)/(average surface roughness) (Sa). The selected processing parameters are laser power, scan speed, hatch spacing, laser pattern increment angle, and heat treatment (HT) condition. The present work revolves around ANN modeling and using a wide parameter range and a large number of test samples under ASTM standards as well as adding HT to the DOE to analyse the simultaneous effect of HT and changing process parameters on surface characteristics. A large and precise data set with high generality and reliability obtained by 3750 profilometries on 125 samples. The contribution of this paper is using ANN as an accurate tool in surface modeling and characterizing the effective parameters on the surface of LPBF parts. The existence phenomena and governing factors were explained by introducing new parametric mechanisms in rheology of melting pool. In AM of metals, the variation of average roughness in overlap of hatches can be 5–7 times higher than the centre of the track. Therefore, Sa was selected to have consistency in the measured roughness values. Results showed heat treatment above beta phase transus leads to a local flow of material at the surface causing an increase of Sa. The ranking of influential factors on Sa from the highest to the lowest was found to be: heat treatment > laser power > scan pattern angle > hatch space > scan speed.