The authors study linear processes of a stationary associated sequence of random vectors, \(X_t= \sum^\infty_{u=0} A_u Z_{t-u}\), where \((A_u)\) is a sequence of \(m\times m\) coefficient matrices and where \((Z_t)_{t\in\mathbb{Z}}\) is a stationary sequence of associated \(m\)-dimensional random vectors. A functional central limit theorem for partial sums of the \((X_t)_{t\geq 0}\)-process is established. The main idea of the proof is to couple the partial sums of the \(X_t\)’s to partial sums of \(\widetilde X_t:= (\sum^\infty_{j=0} A_j)Z_t\), and to apply the functional CLT of R. M. Burton, A. R. Dabrowski and H. Dehling [Stochastic Processes Appl. 23, 301-306 (1986; Zbl 0611.60028)].