To examine the relationship between the adsorption isotherm and the freezing behavior of a confined Kr, we performed measurements of adsorption-desorption isotherms in a wide temperature range 82-110 K for Kr confined in the cylindrical pores of SBA-15 with a mean radius of 3.2 nm, as well as simultaneous measurements of adsorption isotherms and X-ray diffraction patterns in a temperature range 80-92 K. Hysteresis loops were observed in the whole temperature range examined here. With increasing temperature, the density of the capillary condensate decreased rapidly in a temperature range 92-98 K, strongly suggesting that the freezing point at complete filling is similar to 92 K. The increase in density of the capillary condensate on freezing was only 4.4% as compared to 15.3% for the bulk phase. The difference of the chemical potential with respect to the bulk solid against T changed continuously in a wide temperature range 94-104 K. Simultaneous measurements of adsorption isotherms and X-ray diffraction patterns showed that the freezing point of the capillary condensate at complete filling was similar to 92 K, in a good agreement with the estimation from the temperature dependence of the density. When crystallization of a capillary liquid occurred, the position of the main peak in the diffraction pattern did not change appreciably. Moreover, crystallization always occurred within the step due to capillary condensation in the adsorption isotherm at the Cemperatures between 80 and 92 K. The minimum amount of the capillary condensate above which crystallization sets in increased with increasing temperature. The nature of the freezing transition and a capillary triple point is considered.