This paper proposes new rational cubic Ball spline interpolant with four parameters. The degree smoothness of the rational interpolant is C1. The rational cubic Ball spline (cubic/cubic) has been used for positivity preserving of positive data. The sufficient conditions for the rational cubic Ball interpolant to be positive are derived. Two parameters acted as free parameters while the other two parameters are dependent parameter. Some numerical results are presented together with comparisons with the existing scheme. Our main findings show that the new rational cubic Ball spline interpolant gives satisfactory results and comparable with existing scheme. © 2015 AIP Publishing LLC.