Abstract A sequential orthogonal approach to the building and training of a neural network with a single radial basis function (RBF) neuron is presented in this paper. A sequential learning neural network model proposed by Zhang and Morris  is used in this paper to tackle the common problem encountered by conventional feed forward neural networks in the determination of the network structure in the number of hidden layers and the number of hidden neurons in each layer. For most of the applications, a single hidden RBF neuron itself will be sufficient and for other complex problems the procedure starts with a single hidden neuron and sequentially increases the number of hidden neurons until the model error becomes sufficiently small. The classical Gram–Schmidt orthogonalization method is used at each step to form a set of orthogonal bases for the space spanned by output vectors of the hidden neuron. It is also possible to determine the necessary number of hidden neurons for the required error. However for the problems investigated in this paper one hidden RBF neuron itself is sufficient to achieve desired accuracy. The neural network architecture has been trained and tested to three practical civil engineering problems such as (1) soil classification and (2) for the prediction of strength and workability of high performance concrete (3) for the prediction of ultimate shear strength of reinforced concrete deep beams.