The complex analytical signal representation was applied to study the free-space propagation of ultrashort pulsed Bessel-Gauss beams with constant diffraction length. Closed-form expressions were derived and analyzed both theoretically and numerically. It is shown that within the diffraction-free range,the spreading of transversal intensity distributions of ultrashort pulsed Bessel-Gauss beams is small,whereas beyond this range a remarkable spreading appears. But,within the diffraction-free range there is still a broadening of on-axis pulse forms. With increasing propagation distance,the on-axis blue shift increases monotonously and then reaches gradually its asymptotic value. The off-axis spectral shift changes from the blue shift to the red one as the transversal distance increases.