Gjelsvik is a surname. Notable people with the surname include:
Agvald Gjelsvik (1907–1976), Norwegian educator and politician Kristin Gjelsvik (born 1986), Norwegian blogger and YouTuber Nikolaus Gjelsvik (1866–1938), Norwegian jurist and law professor Olav Gjelsvik (born 1956), Norwegian philosopher Sigbjørn Gjelsvik (born 1974), Norwegian politician