  We build and train the artificial neural network model (ANN) based on the
experimental $\alpha$-decay energy ($Q_{\alpha}$) data. Besides decays between
the ground states of parent and daughter nuclei, decays from the ground state
of parent nuclei to the excited state of daughter nuclei are also included. By
this way, the number of samples are increased dramatically. The results
calculated by ANN model reproduce the experimental data with a good accuracy.
The root-mean-square (rms) relative to the experiment data is 0.105 MeV. The
influence of different input is investigated. It is found that either the shell
effect or the pairing effect results in an obvious improvement of the
predictive power of ANN model, and the shell effect plays a more important
role. The optimal result can be obtained as both the shell and pairing effects
are considered simultaneously. Application of ANN model in prediction of the
$\alpha$-decay energy shows the neutron magic number at $N=184$, and a possible
sub-shell gap around $N=174$ or 176 in the superheavy nuclei region.
