Database parameter automatic tuning is one of the challenging and difficult tasks that database administrators (DBAs) frequently encounter in artificial intelligence (AI) enabled database (DB) systems. Preferentially optimizing key parameters emerges as a critical point in addressing this issue, and it can help identify important parameters by exploring the interactions between parameters. Aiming to overcome the disadvantages of existing methods, we propose a collaborative multi-agents model called CMA+DB to automatically tune DB parameters in an effective and efficient fashion. CMA+DB integrates three components including SAPM (Single-Agent Pre-trained Model), MATM (Multi-Agent Joint Training Model), and PJTM (Probability-based Joint Training Model). SAPM applies the deep deterministic policy gradient to explore the impact of one single agent on DB performance, MATM uses multi-agent deep deterministic policy gradients to find agents that collaboratively work to improve DB performance, and PJTM can enhance parameter tuning by important agents based on a probabilistic selection factor. In the CMA+DB model, each agent is responsible for tuning a portion of the parameters, and multiple agents collaborate to recommend the optimal parameter configuration. This hybrid model can expand the number of tunable parameters in order to perform parameter tuning from the aspects of functions and parameter levels (i.e., global, DB, and session level). Experimental results reveal that CMA+DB obtains the fastest convergence performance (when reaching the largest throughput) of 14.83% faster than the state-of-the-art (SOTA) algorithms in the TPC-C benchmark on average. Essentially, after the phase of SAPM model training, CMA+DB outperforms the performance of the SOTA models in throughput. Furthermore, DB performance of CMA+DB can be improved by 1.758% through the phases of MATM and PJTM model training.