Let S be a subset of V ( G ). The vertices of S are colored black and the vertices of V ( G ) - S are colored white. The color-change-rule is defined as if there is a black vertex u having an unique white neighbor v , then change the color of v to black. The zero forcing number of a graph, denoted by Z ( G ), is the minimum cardinality of a set S such that all vertices of V ( G ) are black by repeating the color-change-rule, which was proposed at the AIM-minimum rank group in 2008 to bound the maximal nullity of G . Hence it has received much attention. Our interest is to study the zero forcing number of graphs with matching number α ′ ( G ) and cyclomatic number c ( G ). In the paper, utilizing the alternating path and an operation associated with a vertex partition, we verify the sharp bounds that n ( G ) - 2 α ′ ( G ) ≤ Z ( G ) ≤ n ( G ) - α ′ ( G ) + c ( G ) - 1 for n ( G ) ≥ 3 . The extremal graphs attain the upper bound are completely characterized.