Inspired by the observation that some real-life networks' sizes grow as a geometric series, a growing complex network model with acceleratingly increasing number of nodes is proposed. At each time step, the number of newly added nodes is proportional to the size of the network. This network shows scale-free property when the growing rate r is not large, and its power-law exponent is tunable from 2 to 3 through r. The average path length decreases and clustering coefficient increases with r respectively. In addition, we also give an analytical solution about power-law exponent versus r that agrees well with the simulation result.