Summary: In an edge-colored graph \((G, c)\), let \(d^c(v)\) be the number of colors on the edges incident to vertex \(v\) and let \(\delta^c(G)\) be the minimum value of \(d^c(v)\) over all vertices \(v \in V(G)\). A cycle of \((G, c)\) is called proper if any two adjacent edges of the cycle have distinct colors. An edge-colored graph \((G, c)\) on \(n \geq 3\) vertices is called properly vertex-pancyclic if each vertex of \((G, c)\) is contained in a proper cycle of length \(l\) for every \(l\) with \(3 \leq l \leq n\). S. Fujita and C. Magnant [ibid. 159, No. 14, 1391–1397 (2011; Zbl 1228.05150)] conjectured that every edge-colored complete graph on \(n \geq 3\) vertices with \(\delta^c(G) \geq \frac{n + 1}{2}\) is properly vertex-pancyclic. We show that this conjecture is true if the edge-colored complete graph has no monochromatic triangles.