The short QT syndrome (SQTS) is a genetic disease of heart which leads to an increased risk of atrial arrhythmias and sudden cardiac death. Cardiac alternans and high-frequency spiral waves are believed to be strongly associated with atrial arrhythmias. The present study aims to use computational models to investigate the alternans and re-entrant spiral wave in SQTS. The Colman-Zhang (CZ) human atria cell model was implemented for simulation. Newly developed IK1 formulations describing the wide type (WT) and two SQTS mutations (D172N and E299V) were incorporated. Alternans was studied in rapid heart beat rate conditions, and the S1-S2 protocol was used to initiated re-entrant excitation wave in 2D tissue. Alternans were found in the intracellular calcium concentration [Ca2+]i traces from basic cycle length (BCL) of 250 to 300 ms, and no alternans was observed in E299V mutation condition. In contrast, alternans emerged when BCL was smaller than 410 ms in WT condition. The minimal spatial lengths of S2 stimulus required to initiate re-entry was reduced by the mutations. Therefore, our findings show that there is a decreased observation of alternans phenomena and the spatial vulnerability to re-entry significantly increased in SQTS conditions.