  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 J_{1} and J_{1'} along x and y directions competing with a
next-nearest-neighbor coupling J_{2} (NNN). The ground state phase diagram in
the ({\lambda},{\alpha}) space, where {\lambda}=J_{1'}/J_{1} and
{\alpha}=J_{2}/J_{1}, is obtained. Depending on the values of {\lambda} and
{\alpha}, we obtain three different states: antiferromagnetic (AF), collinear
antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate
region {\lambda}_{1}<{\lambda}<1 we observe a QP state between the ordered AF
and CAF phases, which disappears for {\lambda} above some critical value
{\lambda}_{1}. 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 AF and CAF phases, with a behavior approximately
described by the classical line {\alpha}_{c}{\simeq}{\lambda}/2.
