This paper leans heavily on Nelson Siegel tested on Nigerian Euro-bond. The objectives of this paper are to obtain the model for (r) the forward rate and spot rate function (it) compute the console rate and (iii) investigate the rationale behind the parallel shift on the predicted yield curve. We selected data at 12 different points from the daily closing of the Nigerian Eurobond from January to December 2018 to fit the Nigerian Eurobond yield curve using the Nelson Siegel model. In order to facilitate a deeper understanding of the term structure approximation model of Nigerian Euro-bond from first principles, our initial data was re-run to permit further interpretation on the estimation and our results show that the variation caused by consol is responsible for the parallel shift on the predicted yield curve indicating that the value of the predicted Eurobond moves up or down in the same direction corresponding to the same degree of the corresponding change in the consol rate. Furthermore, based on the upward sloping behavior of the yield curve, the Nigerian economy is expanding and consequently, long-term investments will tend to be very risky.