This paper proposes a novel algorithm using an artificial neural network for modeling simultaneously both a 3-D flow velocity vector and a concentration field. The neural network is trained so that four outputted values of the network, three components of a 3-D velocity vector and a concentration of substances such as air pollutants or bacilli, agree with measured ones and additionally the continuity and diffusion equations are satisfied in the flow field. An approximate model for the velocity and concentration field can be constructed in the neural network from sparsely measured data. When any 3-D position, (x, y, z), is inputted to the neural network model, it outputs a 3-D velocity vector and a concentration at the position. The entire 3-D velocity vector and concentration field, therefore, can be easily estimated using the model. To validate the algorithm, the smoke concentration distribution estimated from a very limited set of measured data is compared with the measured one in which most of the data is unused for the modeling. Even from sparsely measured velocity vectors and smoke concentrations, the novel algorithm gives the entire concentration distribution whose flow characteristics are almost similar to the experimental result.