Prompt tuning is a promising method to fine-tune a pre-trained language model without retraining its large-scale parameters. Instead, it attaches a soft prompt to the input text, whereby downstream tasks can be well adapted by merely learning the embeddings of prompt tokens. Nevertheless, existing methods still suffer from two challenges: (i) they are hard to balance accuracy and efficiency. A longer (shorter) soft prompt generally leads to a better (worse) accuracy but at the cost of more (less) training time. (ii) The performance may not be consistent when adapting to different downstream tasks. We attribute it to the same embedding space but responsible for different requirements of downstream tasks. To address these issues, we propose an Efficient Prompt Tuning method (EPT) by multi-space projection and prompt fusion. Specifically, it decomposes a given soft prompt into a shorter prompt and two low-rank matrices, whereby the number of parameters is greatly reduced as well as the training time. The accuracy is also enhanced by leveraging low-rank matrices and the short prompt as additional knowledge sources to enrich the semantics of the original short prompt. In addition, we project the soft prompt into multiple subspaces to improve the performance consistency, and then adaptively learn the combination weights of different spaces through a gating network. Experimental experiments on 13 natural language processing downstream tasks show that our method significantly and consistently outperforms 11 comparison methods with the relative percentage of improvements up to 28.8%, and training time decreased by 14%.