Transformers in modern power systems often experience different types of faults due to electrical, mechanical, and thermal stresses during their service life. In this regard, online diagnosis is particularly important to ensure reliable and economic operation of power system by avoiding equipment damages and outages. In this work, a new methodology for online diagnosis of inter-turn faults in transformers is presented. In general, the proposal determines the fault condition through the differential current spectrum and a fuzzy logic (FL) system. For the spectrum estimation, a phasor measurement unit (PMU)-based scheme is expanded to a harmonic PMU (HPMU)-scheme to obtain the magnitude and phase of the harmonic content for the voltage and current signals in a synchronized way. The FL system diagnoses the transformer condition in a continuous and online way. As the proposed method is focused on the online diagnosis of fault, its performance is tested under different operating conditions, including no-load, linear loads, and non-linear loads. To increase the analysis, a simulated three-phase transformer and a real single-phase transformer that present different levels of fault severity for the inter-turn fault condition are analyzed. Results show the effectiveness and usefulness of the proposal.