Remote Myocardial Infarction (RMI) monitoring uses electronic devices to detect the electrocardiogram changes and inform the doctor in emergency conditions, which is an effective solution to save the patient's life. In this paper, we propose the Multi-Channel Lightweight CNN (MCL-CNN), which combines electrocardiogram signals from four leads (v2, v3, v5 and aVL) to detect the Anterior MI (AMI). Its multi-channel design allows the convolution of each lead to be independent of each other, and allowing them to find the filter that best suits them. In addition, constructing a lightweight network using different convolutional combinations in the MCL-CNN model, which makes the network has certain advantages in computing runtime parameters and more suitable for mobile devices. Meanwhile, we use balanced cross entropy to solve the problem of dataset class imbalance. These strategies make the MCL-CNN suitable for multi-lead ECG processing. Experimental results using public ECG datasets obtained from the PTB diagnostic database demonstrate that MCL-CNN's accuracy is 96.65%.