Active tracking of space noncooperative object that merely relies on vision camera is greatly significant for autonomous rendezvous and debris removal. Considering its Partial Observable Markov Decision Process (POMDP) property, this paper proposes a novel tracker based on deep recurrent reinforcement learning, named as RAMAVT which drives the chasing spacecraft to follow arbitrary space noncooperative object with high-frequency and near-optimal velocity control commands. To further improve the active tracking performance, we introduce Multi-Head Attention (MHA) module and Squeeze-and-Excitation (SE) layer into RAMAVT, which remarkably improve the representative ability of neural network with almost no extra computational cost. Extensive experiments and ablation study implemented on SNCOAT benchmark show the effectiveness and robustness of our method compared with other state-of-the-art algorithm. The source codes are available on https://github.com/Dongzhou-1996/RAMAVT.