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A numerical model is developed to study the temporal evolution of helicon discharge. The initiation of helicon discharge is first presented in terms of time-dependent electron density and temperature, electric and magnetic fields, and power deposition; then, their steady-state values are compared with experimental data and previous simulations for benchmark. It is found that the evolutions of electron density and temperature arrive steady state around 100 and $1.5~\mu \text{s}$ , respectively, while electric and magnetic fields become steady prior to 2 $\mu \text{s}$. The spatial distributions of power deposition indicate that RF power is absorbed mostly near the edge, similar to those of electron temperature. Parameter studies show that high background pressure, confining magnetic field strength, and RF power are beneficial to obtaining high-density helicon plasma, while the driving frequency has little effect. These findings are interesting for the design and optimization of helicon plasma source. [ABSTRACT FROM AUTHOR]