The principle of minimum dissipation rate is applied to tokamak plasmas with energy and helicity balances imposed as two constraints. The analytical solution on toroidal current distribution are derived from the resulting Euler-Lagrangian equation. Three typical forms of current profiles are found for low-aspect-ratio tokamaks like NSTX. One of them decreases with r on equatorial plane, the second peaks in the inner half part on equatorial plane and the third may have a hole or reverse in the central part. The principle of minimum dissipation rate is applied to tokamak plasmas with energy and helicity balances imposed as two constraints. The analytical solution on toroidal current distribution are derived from the resulting Euler-Lagrangian equation. Three typical forms of current profiles are found for low-aspect -ratio tokamaks like NSTX. One of them decreases with r on equatorial plane, the second peaks in the inner half part on equatorial plane and the third may have a hole or reverse in the central part.