The ion current from an electron cyclotron resonance (ECR) heavy ion source depends on the confining axial and radial magnetic fields. Some efforts were made by earlier workers to investigate magnetic field scaling on the performance of the ECR source. In order to study the dependence of the ion current on the injection magnetic field in the 6.4 GHz ECR source, we have measured the current by varying the peak injection field and have inferred that the variation of the current is exponential up to our maximum design injection field of 7.5 kG. An attempt has been made to understand this exponential nature on the basis of ion confinement time.