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In the present work, the current-voltage (I-V) characteristics in a coupled long Josephson junction based on magnesium diboride are studied by establishing a system of equations of phase differences of various inter- and intra-band channels starting from the microscopic Hamiltonian of the junction system and simplifying it through the phenomenological procedures such as action, partition function, Hubbard-Stratonovich transformation (bosonization), Grassmann integral, saddle-point approximation, Goldstone mode, phase dependent effective Lagrangian and, finally, Euler-Lagrange equation of motion. The system of equations are solved using finite difference approximation for which the solution of unperturbed sine-Gordon equation is taken as the initial condition. Neumann boundary condition is maintained at both the ends so that the fluxon is capable of reflecting from the end of the system. The phase dependent current is calculated for different tunnel voltage and averaged out over space and time. The current-voltage characteristics are almost linear at low voltage and non-linear at higher voltage which indicates that the more complicated physical phenomena at this situation may occur. At some region of the characteristics, there exist a negative resistance which means that the junction system can be used in specific electronic devices such as oscillators, switches, memories etc. The non-linearity is also sensitive to the layer as well as to the junction thicknesses. Non-linearity occurs for lower voltage and for higher junction and layer thicknesses., Comment: 17 pages, 7 figures