The alpha --> beta transformation behavior and the temperature dependence of lattice strain of alpha-AgI crystal frozen in an AgI-based orthoborate glass matrix were investigated by differential scanning calorimetry and x-rag diffraction in the temperature range from 20 to 180 degrees C. After heating to various temperatures, the glass matrix strongly suppressed the alpha --> beta transformation during cooling. The alpha --> beta transformation temperatures decreased with decreasing maximum heating temperatures. The alpha-AgI crystal frozen in the orthoborate glass matrix could not transform during cooling if the maximum heating temperature was lower than the glass transition temperature (T-g) of the matrix glass. The suppressing effect of alpha --> beta transformation of the glass matrix was-suggested to become stronger with decreasing maximum heating temperature. The heterogeneous lattice strain of frozen alpha-AgI was large when the composite was kept at temperatures below T-g, and became smaller at temperatures above T-g, in the heating process. The alpha --> beta transformation occurred only during cooling after the lattice strain of alpha-AgI was suffieiently released by heating to temperatures above T-g of the matrix glass. The large lattice strain of frozen alpha-AgI and the value of T-g mainly affected the transformation behavior of alpha-AgI in the glass matrix.