Multi-parametric magnetic resonance imaging (MRI) can provide complementary quantitative information by generating multi-parametric maps and is becoming a promising imaging technique for advanced medical diagnosis. However, multi-parametric MRI requires longer acquisition time than normal MRI scanning. The existing reconstruction methods for accelerated multi-parametric MRI suffer from suboptimal performance due to stage-wise optimization, and inefficient utilization of intra- and inter-contrast information. To address these challenges, we propose an all-in-one joint Sampling, Reconstruction, and Mapping network, dubbed as SRM-Net, for multi-parametric MRI reconstruction on multi-coil and multi-contrast MR images. Specifically, our model consists of three modules including sampling, reconstruction, and mapping. In the sampling module, we introduce a sampling scheme to generate individually-optimized sampling pattern across multi-contrast images. In the reconstruction module, we adopt a spatio-temporal attention mechanism, which is embedded in a dual-domain-based unrolling framework, to better exploit inter- and intra-contrast correlations. In the mapping module, we employ multi-layer perceptron to model complex nonlinear mapping. Integrating Sampling, Reconstruction, and Mapping, our SRM-Net enables the end-to-end learning paradigm. Experimental results show that our SRM-Net generates superior multi-parametric maps including T1, T2 * and PD for brain on 3T MR scanner compared to state-of-the-art methods, and meanwhile provides promising intermediate weighted MR images.