Let \(G\) be a finite simple graph with vertex set \(V(G) = \{v_1, \dots, v_n\}\) and edge set \(E(G)\). Also, let \(S = \mathbb{K}[x_1, \dots, x_n, y_1, \dots, y_n]\) be the polynomial ring over a field \(\mathbb{K}\). The binomial edge ideal of \(G\), denoted by \(J_G\) is an ideal of \(S\) which is generated by binomials of the form \(f_{ij} = x_iy_j-x_jy_i\), where \(i < j\) and \(\{v_i, v_j\}\) is an edge of \(G\). From an algebraic viewpoint, it is of interest to study relations between algebraic properties of \(J_G\) and combinatorial properties of \(G\). In the paper under review the author proves that Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.