We study the rotational wave packet created by nonadiabatic rotational excitation of molecules with strong femtosecond laser pulses. The applicable condition of the Delta-Kick method is obtained by comparing the laser intensity and pulse duration dependences of the wave packet calculated with different methods. The wave packet evolution is traced analytically with the Delta-Kick method. The calculations demonstrate that the rotational populations can be controlled for the rotational wave packet created by two femtosecond laser pulses. The evolution of the rotational wave packet with controlled populations produces interference patterns with exotic spatial symmetries. These calculations are validated by comparing the theoretical calculations with our experimental measurements for the rotational wave packet created by thermal ensemble CO2 and two strong femtosecond laser pulses. Potential applications in molecular science are also discussed for the rotational wave packet with controlled populations and spatial symmetries.