Let T_ be the Toeplitz operator defined on the Fock space L2 a(C) with symbol _ ∈ L∞(C). Let for _ ∈ C, k_(z) = e ¯_ z 2 −|_|2 4 , the normalized reproducing kernel at _ for the Fock space L2 a(C) and t_(z) = z −_, z, _ ∈ C. Define the weighted composition operator W_ on L2 a(C) as (W_f)(z) = k_(z)(f ◦ t_)(z). In this paper we have shown that if M and H are two bounded linear operators from L2 a(C) into itself such that MT H = T ◦t_ for all ∈ L∞(C), then M and H must be constant multiples of the weighted composition operator W_ and its adjoint respectively.