Reservoir computing (RC), as an efficient training paradigm for recurrent neural networks (RNNs), performs excellently on single time series tasks. However, in multi-task scenarios, reservoir states induced by different tasks tend to overlap, limiting its application. To address this issue, this paper proposes a multi-task reservoir computing framework based on subspace mapping, and building upon the traditional echo state network (ESN), designs and implements a multi-task echo state network (MT-ESN). This method assigns a unique binary mapping vector to each task. At each time step, the original reservoir state corresponding to a task undergoes a Hadamard product operation with its mapping vector. This selectively projects the original high-dimensional reservoir state into a low-dimensional subspace defined by its mapping vector, thereby achieving structured separation of different task's reservoir state trajectories within the shared reservoir. This fundamentally suppresses the phenomenon of state overlap and effectively reduces the degree of overlap between states of different tasks. Through experimental validation on short-term prediction of multiple chaotic attractors and multiple real-world time series predictions, compared to the standard ESN, the MT-ESN significantly enhances the accuracy and stability of multi-task processing within a single reservoir network. Particularly in long-term prediction, it effectively avoids state collapse. t-distributed stochastic neighbor embedding (t-SNE) visualization also confirms its reservoir state separation capability. The study further reveals that there exists an optimal sparsity for the mapping vectors. The proposed method provides an effective approach for implementing multi-functional reservoir computing on resource-constrained devices.