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A superconducting magnet system that consists of a cable-in-conduit conductor (CICC) coil and two NbTi solenoid coils is being developed. The superconducting magnet will be capable of generating a central magnetic field of 12 T. The stored energy of the magnet is 2.05 MJ. As a result of possible misalignment between the coil and NbTi coils during installation, there exists a radial or axial force between two types of coils. In this paper, we use the Grover's formulas with filament method to calculate the mutual inductance and its gradient between coils. Based on this method, we apply the mutual inductance gradient method to calculate the radial and axial force between coils. We confirm the validity of this method by comparing it with an exact 3-D semianalytical expression on axial force for coaxial but midplane offset coils. Results obtained by two methods are in excellent agreement. All results obtained on radial and axial forces are introduced.