Let q be a prime power. Following a paper by Coons, Jenkins, Knowles, Luke and Rault (case q a prime ) we define the numerical range Num(M)⊆Fq2 of an n×n-matrix M with coefficients in Fq2 in terms of the usual Hermitian form. We prove that ♯(Num(M))>q (case q≠2), unless M is unitarily equivalent to a diagonal matrix with eigenvalues contained in an affine Fq-line. We study in details Num(M) when n=2.