利用缓变包络近似，给出了一组傍轴波动方程的解析解,该解可以表示一组新型超短脉冲光束，即超短双曲余弦高斯脉冲光束。对超短双曲余弦高斯脉冲光束在自由空间的传输性质进行了详细的研究，给出了传输时的轴向光强、横向光强分布、极性反转、脉冲时间延迟、功率谱等。结果表明，超短双曲余弦高斯脉冲光束的轴上光强随着传输距离的增加而平滑地减小。双曲余弦函数的参数对脉冲光束的空间强度分布及脉冲宽度都有影响。给出了超短双曲余弦高斯脉冲光束功率谱的解析表达式，研究表明随着双曲余弦函数参数的变大，功率谱会分裂成几个峰，远离光束中心的边缘会出现红移现象。

A family of ultrashort pulsed beams named ultrashort pulsed hyperbolic-cosine Gaussian beams is proposed and the solutions of the paraxial wave equation are given in theory by using slowly varying envelope approximation. The propagation properties of the intensity along the axis, the transversal intensity distribution, the polarity reversal, the pulse time delay and the power spectrum of the hyperbolic-cosine Gaussian beam in free space are studied systematically. It is found that the on-axial intensity decreases smoothly with the increasing of the propagation distance, and the parameter of hyperbolic-cosine function affects the maximum spatial intensity and the pulse width. Furthermore, the split of the power spectrum with the increasing of the hyperbolic-cosine function parameter and the red-shift on the beam periphery are also observed.