This paper addresses the design of reduced-order interval-observers for dynamic systems with time-invariant uncertainty. Because of the limitations of using the set-based approach to preserve the time dependency of parameter uncertainty and the wrapping effect to deal with interval-observers, the trajectory-based interval-observer approach is used with an appropriate observer gain. But, there could be some difficulties to satisfy the conditions for selecting a suitable gain to guarantee the positivity of the resulting observer. Then, a reduced-order observer is designed to reduce the computational complexity and to increase the degree of freedom when selecting the observer gain. Finally, a simulation example is employed for illustrating and analyzing the effectiveness of the proposed approach.