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In this letter, the state estimation problem is dealt with for delayed genetic regulatory networks (GRNs) with SUM logic and multiple sensors. Time delays here are assumed to be time-varying and belong to the given intervals. The genetic regulatory functions are supposed to satisfy the sector-like condition. We aim to design a distributed state estimator which approximates the genetic states through the measurements of the sensors, i.e., the estimation error system is globally asymptotically stable. Based on the Lyapunov functional method, it is shown that if a set of linear matrix inequalities (LMIs) are feasible, the desired distributed state estimator does exist. A numerical example is constructed in the end of the paper to demonstrate the effectiveness of the obtained criteria.