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The recording of electrical activity of the heart by using electrodes is known as electrocardiography (ECG). In long time monitoring of ECG, a huge amount of data needs to be handled. To handle the situation, an efficient compression technique which can retain the clinically important features of ECG signal is required. The continuous monitoring of this signal requires a large amount of memory. Hence, there is a requirement of compression. The compression of ECG signal using transforms in cascade is explored to incorporate the added advantages of both the transforms. This paper presents compression of ECG signal by hybrid technique consisting of cascade and parallel combination of discrete cosine transform (DCT) and discrete wavelet transform (DWT). The simulation is carried out using MATLAB tool. Various wavelet transforms are used for the testing purpose. The performance measures used are Percent square mean Root Difference (PRD) and CR to validate the results. The methodology using cascade combination proved to be better than the parallel technique in terms of Compression Ratio (CR). The highest CR achieved is 28.2 in the method using DCT and DWT in cascade. Different DWTs are used for the testing purpose. The parallel method shows the improved PRD as compared to the cascade method.