In this paper, we introduce the concept of hybrid single-valued neutrosophic number, whose basic units are truth, falsity and indeterminacy memberships, and their properties are investigated. Then, we give the hybrid single-valued neutrosophic whose coefficients are consecutive Fibonacci and Lucas. Especially for consecutive coefficient Fibonacci and Lucas hybrid single-valued neutrosophic numbers, fundamental properties and identities such as Tagiuri, d'Ocagne, Catalan, and Cassini are given. We obtain the Binet formula and generating function formula for these numbers. Moreover, we give some sums of the consecutive coefficient Fibonacci and Lucas hybrid single-valued neutrosophic numbers.