Drop-on-demand (DOD) bioprinting has been widely used in tissue engineering due to its highthroughput efficiency and cost effectiveness. However, this type of bioprinting involves challenges such as satellite generation, too-large droplet generation, and too-low droplet speed. These challenges reduce the stability and precision of DOD printing, disorder cell arrays, and hence generate further structural errors. In this paper, a multi-objective optimization (MOO) design method for DOD printing parameters through fully connected neural networks (FCNNs) is proposed in order to solve these challenges. The MOO problem comprises two objective functions: to develop the satellite formation model with FCNNs; and to decrease droplet diameter and increase droplet speed. A hybrid multi-subgradient descent bundle method with an adaptive learning rate algorithm (HMSGDBA), which combines the multisubgradient descent bundle (MSGDB) method with Adam algorithm, is introduced in order to search for the Pareto-optimal set for the MOO problem. The superiority of HMSGDBA is demonstrated through comparative studies with the MSGDB method. The experimental results show that a single droplet can be printed stably and the droplet speed can be increased from 0.88 to 2.08 m·s^-1 after optimization with the proposed method. The proposed method can improve both printing precision and stability, and is useful in realizing precise cell arrays and complex biological functions. Furthermore, it can be used to obtain guidelines for the setup of cell-printing experimental platforms.