Detection of peaks of different waves of a finger-ECG signal is important for biomedical and biometrics applications. We introduce the augmented-Hilbert transform of first derivative of signal to signify the peaks by suppressing the non-peaks and noisy peaks. We need two computationally simple steps for the detection of peaks: signal transformation and finding local maxima-minima. This method needs computational time O(n log n) for a signal of n samples. The method was tested by a large database of finger-ECG records captured with a handheld ECG device. Experimental results suggest that proposed transform is robust for detection of different peaks. The efficiency and robustness of proposed transform make it suitable for real applications of finger-ECG signal such as atrial fibrillation detection and biometric authentication.