Objective: This study aims to develop a highly accurate method for predicting α-decay energies (Q_α) of superheavy nuclei (SHN) and to identify the region of enhanced stability (the "island of stability") based on α-decay properties. Improving the precision of Q_α calculations is crucial for reliably predicting α-decay half-lives, which are essential for identifying newly synthesized superheavy elements. Methods: A modified Liquid-Drop Model (LDM) formula for calculating Q_α is proposed, eliminating explicit dependence on magic numbers to enhance universality. However, the initial LDM formula alone yields a high root-mean-square deviation (RMSD) of 663.5 keV when compared to experimental Q_α values from the AME2016 database for 369 nuclei with Z ≥ 82. To significantly improve accuracy, a neural network (NN) approach is integrated with the LDM formula. A feedforward backpropagation (BP) neural network with a 2-21-1 architecture (2 input neurons: proton number Z and mass number A; 21 hidden neurons; 1 output neuron: , the correction term is developed. The network is trained using the Levenberg-Marquardt algorithm on a dataset of 369 nuclei (319 training, 50 validation). The final Q_α prediction is given by Q_α^NN = Q_α^Eq.(2) +δQ_α. The Unified Decay Law (UDL) formula (Eq. 8) is then used to calculate α-decay half-lives (T_1/2), both with and without NN correction (denoted UDL and UDL^NN).