Variational quantum eigensolvers (VQEs) have emerged as leading hybrid quantum-classical algorithms for estimating the ground-state energies of molecular Hamiltonians, particularly for noisy intermediate-scale quantum devices. This paper proposes an Automatic Operator Designer which is a self-adaptive search framework for VQEs. The quantum circuits are denoted as operators, with an initial gate set, from which new operators are recursively generated by combining existing ones. A hybrid judgment gate, based on empirical rules and a recurrent neural network (RNN), evaluates candidate circuits by predicting their post-optimization energy and structural effectiveness. Only eligible operators are retained and inserted into the evolving operator pool. Experiments are constructed on hydrogen ( \(H_2\) ) systems under both noiseless and noisy environments, and the Automatic Operator Designer for VQE achieves encouraging performance in reducing circuit depth while maintaining chemical accuracy.