  In this note, we investigate pluri-half-anticanonical systems on the so
called LeBrun twistor spaces. We determine its dimension, the base locus,
structure of the associated rational map, and also structure of general
members, in precise form. In particular, we show that if n>2 and m>1, the base
locus of the system |mK^{-1/2}| on nCP^2 consists of two non-singular rational
curves, along which any member has singularity, and that if we blow-up these
curves, then the strict transform of a general members of |mK^{-1/2}| becomes
an irreducible non-singular surface. We also show that if n>3 and m>n-2, then
the last surface is a minimal surface of general type with vanishing
irregularity. We also show that the rational map associated to the system
|mK^{-1/2}| is birational if and only if m> n-2.
