Kallmann syndrome (KS) is a combination of isolated hypogonadotropic hypogonadism (IHH) with olfactory dysfunction, representing a heterogeneous disorder with a broad phenotypic spectrum. The genetic background of KS has not yet been fully established. This study was conducted on 46 Polish KS subjects (41 males, 5 females; average age: 29 years old). The studied KS patients were screened for defects in a 38-gene panel with next-generation sequencing (NGS) technology. The analysis revealed 27 pathogenic and likely pathogenic (P/LP) variants, and 21 variants of uncertain significance (VUS). The P/LP variants were detected in 20 patients (43.5%). The prevalence of oligogenic P/LP defects in selected genes among KS patients was 26% (12/46), whereas the co-occurrence of other variants was detected in 43% (20 probands). The examined KS patients showed substantial genotypic and phenotypic variability. A marked difference in non-reproductive phenotypes, involving defects in genes responsible for GnRH neuron development/migration and genes contributing to pituitary development and signaling, was observed. A comprehensive gene panel for IHH testing enabled the detection of clinically relevant variants in the majority of KS patients, which makes targeted NGS an effective molecular tool. The significance of oligogenicity and the high incidence of alterations in selected genes should be further elucidated.