The offset quadrature phase-shift keying (OQPSK) modulation is a key factor for the technique of ZigBee, which has been adopted in IEEE 802.15.4 for wireless communications of Internet of Things (IoT) and Internet of Vehicles (IoV), etc. In this paper, we propose the general conditions of pulse shaping filters (PSFs) with constant envelope (CE) property for OQPSK modulation, which can be easily leveraged to design the PSFs with CE property. Based on these conditions, we further design an advanced PSF called $\alpha$-half-sine PSF. It is verified that the newly designed $\alpha$-half-sine PSF can not only keep the CE property for OQPSK but also achieve better performance than the traditional PSFs in certain scenarios. Moreover, the $\alpha$-half-sine PSF can be simply adjusted to achieve a flexible performance tradeoff between the transition roll-off speed and out-of-band leakage.