The competition between α-decay and spontaneous fission of superheavy nuclei (SHN) is investigated by the generalized liquid drop model (GLDM) and the modified Swiatecki's formula respectively.The theoretical decay modes are in good agreement with the experimental results.Predictions are made for as-yet unobserved superheavy nuclei.The theoretical calculations show that the nuclei 298120,295119,290118,291117,287117,294116,289116,286116,285116,284115,283115,283114,282114,280113,276112,275112,274112,273111,272110,265109 may be synthesized experimentally in the near future since they not only have relatively large predicted cross sections but can also be identified via α-decay chains.