Psoriasis is a chronic skin disease that affects millions of people worldwide. In 2014, psoriasis was recognized by the World Health Organization (WHO) as a serious non-communicable disease. In this study, a systems biology approach was used to investigate the underlying pathogenic mechanism of psoriasis and identify the potential drug targets for therapeutic treatment. The study involved the construction of a candidate genome-wide genetic and epigenetic network (GWGEN) through big data mining, followed by the identification of real GWGENs of psoriatic and non-psoriatic using system identification and system order detection methods. Core GWGENs were extracted from real GWGENs using the Principal Network Projection (PNP) method, and the corresponding core signaling pathways were annotated using the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. Comparing core signaling pathways of psoriasis and non-psoriasis and their downstream cellular dysfunctions, STAT3, CEBPB, NF-κB, and FOXO1 are identified as significant biomarkers of pathogenic mechanism and considered as drug targets for the therapeutic treatment of psoriasis. Then, a deep neural network (DNN)-based drug-target interaction (DTI) model was trained by the DTI dataset to predict candidate molecular drugs. By considering adequate regulatory ability, toxicity, and sensitivity as drug design specifications, Naringin, Butein, and Betulinic acid were selected from the candidate molecular drugs and combined into potential multi-molecule drugs for the treatment of psoriasis.