The modulator frequency and output power directly affect the communication rate and link distance in the space optical communications. Considering two specifications of high modulation frequency and high output optical power, a method of adopting transverse modulation and combined modulation is proposed, and LiNbO3(LN) crystal structure and parameter optimization, optical coupling design and power calculation, RF-driven source design, technical analysis of automatic bias are carried out. A laser modulator is designed whose maximum modulation frequency is up to 1238 MHz, output optical power is greater than 1 W, half-wave voltage is about 266 V, maximum phase delay is about 1.39 rad, reduction factor is about 0.99, and extinction ratio is about 20 dB. Experiments show that the theoretical design is consistent with experimental results, and the laser modulator can be applied to the space optical communication demonstration experiments on the ground whose bit error rate is better than 10-9 and the link distance is more than 7 km. It can also be applied in the near space or deep space optical communications.