A non-empty k-regular graph Γ on n vertices is called a Deza graph if there exist constants b and a(b≥a) such that any pair of distinct vertices of Γ has either b or a common neighbours. The quantities n, k, b, and a are called the parameters of Γ and are written as the quadruple (n,k,b,a). If a Deza graph has diameter 2 and is not strongly regular, then it is called a strictly Deza graph. In the present paper, we investigate strictly Deza graphs whose parameters (n,k,b,a) satisfy the conditions k=b+1 and [Formula presented] >1.