In this contribution, a new approach to design interval observer for continuous-time linear systems is introduced. First, a more general structure than the classical Luenberger observer is proposed and extended to the interval case based on an explicit set integration method. Then, to obtain tight state enclosures, the computation of the design matrices involved in this new structure is formulated as a nonlinear constrained optimisation problem. In addition, using the symmetric property of interval vectors, a less complex form of the proposed interval observer is presented. On the other hand, compared to the conventional interval observers, no preserving order property on the dynamics of the estimation error is required to apply the introduced method. A numerical case study example is considered to illustrate the effectiveness of the proposed method and to compare its performance to that of a former method.