Let $A,B$ be $n\times n$ (complex) matrices. We are mainly interested in the study of the structure of the spectrum of a linear pencil, that is, a pencil of the form $A-\lambda B$, where $\lambda$ is a complex number. Our main purpose is to obtain spectral inclusion regions for the pencil based on numerical range. The numerical range of a linear pencil of a pair $(A, B)$ is the set $W(A,B) = \lbrace x^{*}(A-\lambda B)x:x \in C^{n}, \left\lVert x \right\rVert = 1,\lambda \in C \rbrace.$ The numerical range of linear pencils with hermitian coefficients was studied by some authors.

We are mainly interested in the study of the numerical range of a linear pencil, $A- \lambda B,$ when one of the matrices $A$ or $B$ is Hermitian and $\lambda \in C.$ We characterize it for small dimensions in terms of certain algebraic curves. The results are illustrated by numerical examples.