We present narrowing calculi that are computation models of functional-logic programming languages. The narrowing calculi are based on the notion of the leftmost outside-in reduction of Huet and Lévy. We note the correspondence between the narrowing and reduction derivations, and define the leftmost outside-in narrowing derivation. We then give a narrowing calculus OINC that generates the leftmost outside-in narrowing derivations. It consists of several inference rules that perform the leftmost outside-in narrowing. We prove the completeness of OINC using an ordering defined over a narrowing derivation space. To use the calculus OINC as a model of computation of functional-logic programming, we extend OINC to incorporate strict equality. The extension results in a new narrowing calculus, s-OINC. We show also that s-OINC enjoys the same completeness property as OINC.