In this study we will consider the construction of approximate optimal design for one-dimensional regression by exchange algorithm. Sufficient conditions under which an optimal design must have the minimal support points are known in Theorem 2.3.2 of Fedorov (1972). However, there are only a few cases which the analytic optimal designs are known. The exchange procedure for computing optimal designs is easily adopted to most criteria. We describe implementations for constructing the well-known special cases D-, A-, and c-optimal designs with the minimum number of support points. Examples which illustrate how the algorithm can be used to obtain these optimal designs and the performance of the algorithm are discussed. The commonly used D-, A-, and c-optimal criteria will be employed to study the convergence properties of the exchange algorithm for regression model which the set of the product of regression functions forms a Chebyshev system.