Accumulating evidence indicates that m6A methyltransferase 3 (METTL3) plays a pivotal role in different malignancies including melanoma. However, the function and underlying mechanisms by which METTL3 contributes to the tumorigenesis of melanoma remain undocumented. The association of METTL3 and long noncoding RNA (lncRNA) small nucleolar RNA host gene 3 (SNHG3) with clinicopathological characteristics and prognosis in patients with melanoma was analyzed by real-time quantitative polymerase chain reaction (RT-qPCR), Western blotting, and The Cancer Genome Atlas data sets. The role of METTL3 in melanoma cells was assessed by in vitro and in vivo experiments. The m6A dot blot, methylated RNA immunoprecipitation (MeRIP), and RT-qPCR were used to verify METTL3-mediated m6A modification of lncRNA SNHG3. The effect of METTL3 on lncRNA SNHG3 was determined by luciferase gene reporter assay, RT-qPCR, and Western blotting. We found that METTL3 was upregulated in melanoma tissue samples and associated with poor survival in patients with melanoma. Knockdown of METTL3 suppressed the growth and invasion of melanoma cells in vitro and in vivo, whereas restored expression of METTL3 promoted these effects. Mechanistic investigations showed that knockdown of METTL3 reduced SNHG3 m6A levels and its messenger ribonucleic acid (mRNA) expression levels. SNHG3 could act as a sponge of microRNA (miR)-330-5p to upregulate the expression of CCHC-type zinc finger nucleic acid binding protein (CNBP). SNHG3 overexpression reversed METTL3-knockdown-caused antitumor effects, miR-330-5p upregulation and CNBP downregulation. SNHG3 had a positive correlation with METTL3 expression but a negative correlation with miR-330-5p expression in melanoma tissue samples. In conclusion, our findings demonstrated that METTL3-mediated m6A modification of lncRNA SNHG3 promoted the growth and invasion of melanoma cells by regulating the miR-330-5p/CNBP axis.