In practical electrocardiogram (ECG) monitoring, there are some challenges in reducing the data burden and energy costs. Therefore, compressed sensing (CS) which can conduct under-sampling and reconstruction at the same time is adopted in the ECG monitoring application. Recently, deep learning used in CS methods improves the reconstruction performance significantly and can removes of some of the constraints in traditional CS. In this paper, we propose a deep compressive-sensing scheme for ECG signals, based on modified-Inception block and long short-term memory (LSTM). The framework is comprised of four modules: preprocessing; compression; initial; and final reconstruction. We adaptively compressed the normalized ECG signals, sequentially using three convolutional layers, and reconstructed the signals with a modified Inception block and LSTM. We conducted our experiments on the MIT-BIH Arrhythmia Database and Non-Invasive Fetal ECG Arrhythmia Database to validate the robustness of our model, adopting Signal-to-Noise Ratio (SNR) and percentage Root-mean-square Difference (PRD) as the evaluation metrics. The PRD of our scheme was the lowest and the SNR was the highest at all of the sensing rates in our experiments on both of the databases, and when the sensing rate was higher than 0.5, the PRD was lower than 2%, showing significant improvement in reconstruction performance compared to the comparative methods. Our method also showed good recovering quality in the noisy data.