  We propose that novel superfluid with supersolid-like properties - angular
stripe phase - can be realized in a pancake-like spin-1/2 Bose gas with
spin-orbital-angular-momentum coupling. We predict a rich ground-state phase
diagram, including the vortex-antivortex pair phase, half-skyrmion phase, and
two different angular stripe phases. The stripe phases feature modulated
angular density-density correlation with sizable contrast and can occupy a
relatively large parameter space. The low-lying collective excitations, such as
the dipole and breathing modes, show distinct behaviors in different phases.
The existence of the novel stripe phase is also clearly indicated in the
energetic and dynamic instabilities of collective modes near phase transitions.
Our predictions of the angular stripe phase could be readily examined in
current cold-atom experiments with $^{87}$Rb and $^{41}$K.
