A path in a vertex-colored graph is a vertex-proper path if any two internal adjacent vertices differ in color. A vertex-colored graph is proper vertexk-connected if any two vertices of the graph are connected by k disjoint vertex-proper paths of the graph. For a k-connected graph G, the proper vertexk-connection number of G, denoted by $$pvc_{k}(G)$$ p v c k ( G ) , is defined as the smallest number of colors required to make G proper vertex k-connected. A vertex-colored graph is strong proper vertex-connected, if for any two vertices u, v of the graph, there exists a vertex-proper u-v geodesic. For a connected graph G, the strong proper vertex-connection number of G, denoted by spvc(G), is the smallest number of colors required to make G strong proper vertex-connected. These concepts are inspired by the concepts of rainbow vertex k-connection number $$rvc_k(G)$$ r v c k ( G ) , strong rainbow vertex-connection number srvc(G), and proper k-connection number $$pc_k(G)$$ p c k ( G ) of a k-connected graph G. Firstly, we determine the value of pvc(G) for general graphs and $$pvc_k(G)$$ p v c k ( G ) for some specific graphs. We also compare the values of $$pvc_k(G)$$ p v c k ( G ) and $$pc_k(G)$$ p c k ( G ) . Then, sharp bounds of spvc(G) are given for a connected graph G of order n, that is, $$0\le spvc(G)\le n-2$$ 0 ≤ s p v c ( G ) ≤ n - 2 . Moreover, we characterize the graphs of order n such that $$spvc(G)=n-2,n-3$$ s p v c ( G ) = n - 2 , n - 3 , respectively. Finally, we study the relationship among the three vertex-coloring parameters, namely, $$spvc(G), \ srvc(G)$$ s p v c ( G ) , s r v c ( G ) , and the chromatic number $$\chi (G)$$ χ ( G ) of a connected graph G.