The phase transition of the quantum spin-1/2 frustrated Heisenberg antiferroferromagnet on an anisotropic square lattice is studied by using a variational treatment. The model is described by the Heisenberg Hamiltonian with two antiferromagnetic interactions: nearest-neighbor (NN) with different coupling strengths J1 and J 1 along x and y directions competing with a next-nearest-neighbor coupling J2 (NNN). The ground state phase diagram in the (γ, a) space, where γ = J'1/J1 and a = J2/J 1, is obtained. Depending on the values of 1 and a, we obtain three different states: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region 1γ < 1 < γ we observe a QP state between the ordered AF and CAF phases, which disappears for 1 above some critical value 1γ=0. 53. The boundaries between these ordered phases merge at the quantum critical endpoint (QCE). Below this QCE there is again a direct first-order transition between the AFand CAF phases, with a behavior approximately described by the classical line a c-γ/2. © 2013 Elsevier Ltd. All rights reserved.