This study presents the first prediction results of a neural network model for the vertical total electron content of the topside ionosphere based on Swarm-A measurements. The model was trained on 5 years of Swarm-A data over the Euro-African sector spanning the period 1 January 2014 to 31 December 2018. The Swarm-A data was combined with solar and geomagnetic indices to train the NN model. The Swarm-A data of 1 January to 30 September 2019 was used to test the performance of the neural network. The data was divided into two main categories: most quiet and most disturbed days of each month. Each category was subdivided into two sub-categories according to the Swarm-A trajectory i.e. whether it was ascending or descending in order to accommodate the change in local time when the satellite traverses the poles. Four pairs of neural network models were implemented, the first of each pair having one hidden layer, and the second of each pair having two hidden layers, for the following cases: 1) quiet day-ascending, 2) quiet day-descending, 3) disturbed day-ascending, and 4) disturbed day-descending. The topside vertical total electron content predicted by the neural network models compared well with the measurements by Swarm-A. The model that performed best was the one hidden layer model in the case of quiet days for descending trajectories, with RMSE = 1.20 TECU, R = 0.76. The worst performance occurred during the disturbed descending trajectories where the one hidden layer model had the worst RMSE = 2.12 TECU, (R = 0.54), and the two hidden layer model had the worst correlation coefficient R = 0.47 (RMSE = 1.57).In all cases, the neural network models performed better than the IRI2016 model in predicting the topside total electron content. The NN models presented here is the first such attempt at comparing NN models for the topside VTEC based on Swarm-A measurements.