In this paper, we study the Sahlqvist-type correspondence theory of modal logic with counting ML( \(\#\) ), within the class of image-finite Kripke frames where each node has finitely many successors. Since in the standard translation of ML( \(\#\) ), we need to use existential second-order quantifiers of binary predicates, the correspondence theory here has a different flavor from existing correspondence theory of modal logic whose formulas have first-order standard translations. We use the definability results by Fu and Zhao to reduce some “essentially second-order” cardinality comparison formulas to graded modal formulas (with countably infinite conjunctions and disjunctions), and thus get the correspondence results for a fragment of ML( \(\#\) )-formulas with corresponding properties written in a first-order language with infinite conjunctions and disjunctions.