Recently, arrhythmogenic condition has attracted special attention of scientists in the field of different disciplines because sudden cardiac death is often caused by cardiac arrhythmia. Arrhythmias can have different underlying causes. But the underlying mechanism of arrhythmia is not fully understood due to cardiac complexity. As is well known, one particular group of arrhythmias is often associated with the afterdepolarizations. So far, afterdepolarizations have been studied mainly in isolated cardiac cells. The question how the afterdepolarization is produced at a tissue level has not been widely studied yet. In this paper, we use the model of human heart to study how spiral wave or other wave patterns induces the afterdepolarizations in two-dimensional myocardial tissue. We try to obtain the instantaneous spatial distribution of afterdepolarizations by changing the L-type calcium and fast potassium conductance. In order to avoid bringing in afterdepolarizations, the applied parameters avoid evoking the afterdepolarizations at a single-cell and one-dimensional tissues level. The numerical simulation results show that spiral wave and other wave patterns can cause the phase II and III early afterdepolarizations, the delayed afterdepolarization, the enhanced automaticity, the delayed excitation and the delayed enhanced automaticity to occur. Moreover, we observe the weak oscillation of the membrane potential during the phase I of action potential. The afterdepolarizations generally occur in the spiral-wave core. They are generated by the phase singularity of spiral wave. The afterpolarizations can also appear in other region of spiral wave pattern. The afterpolarization is characterized by scattered distribution. When parameters are appropriately chosen, we observe the outbreaks of different afterpolarizations under the state of spiral wave. The corresponding spatial and temporal distributions of the early afterdepolarizations, the delayed afterdepolarizations, and the enhanced automaticity become spiral line distributions, which exhibits memory effect. It is shown that the outbreaks of afterdepolarizations in the system do not necessarily lead to the breakup of spiral wave. By observing the changes of different ion currents we find that when sodium current exciting cell is very small, the weak excitation with small sodium current can cause the L-type calcium current and the sodium calcium exchange current to increase, and the slow potassium current and rapid potassium current to decrease, leading to the occurrences of various afterdepolarizations. Therefore, increasing sodium current can effectively suppress the occurrences of afterdepolarizations.