The phase diagram of the spin 1 quantum van Hemmen spin glass model with biaxial crystal-field anisotropy and a transverse magnetic field is studied. We investigate the effects of the two transverse crystal-field parameters (
Dx and
Dy) and transverse field $(\ensuremath{\Omega})$ on the phase diagrams in the $T\ensuremath{-}{D}_{x}$ plane for various values of
Dy and $\ensuremath{\Omega}$. Tricritical and reentrant behavior can be seen for appropriate ranges of these parameters.