Time synchronization for wireless sensors is important for a proper interpretation of measurements, particularly for acceleration measurements to estimate mode-shapes. This paper presents a new time synchronization method working independently on each node without exchanging time-sync packets among nodes. This stand-alone operation can make field measurement campaigns very time-efficient without constructing and validating the wireless sensor network. The proposed method firstly time-stamps measurements using the accurate time-source from a GPS module on each node, and secondly re-samples the time-stamped data to get time-synchronized data. The time-stamping method proposed in the study utilizes Pulse-Per-Second (PPS) signals and NMEA (National Marine Electronics Association) sentences generated by a low-cost GPS module, and the internal timer/counter unit of Arduino. Error analysis on the proposed time-stamping method was carried out and derived an analytical expression for the maximum variance of time-stamping error of the proposed method. Four experiments have been carried out to observe (1) the long-term operational stability of the GPS module, (2) the accuracy of the PPS signals, (3) the accuracy of the proposed time-stamping method, and (4) the validity of the proposed time-synchronization method for output-only modal analysis on a laboratory floor structure. The GPS module was found to operate or to resume operating stably for the entire test period of 7 days even with the limited field of view to the sky. The relative time errors of two PPS signals from four GPS modules were found to be within ±400 ns. The time-stamping error measured by two identical time-stamping Arduinos for common trigger signals was found to have a standard deviation of 40.8 ns, which agreed well with the maximum value of 42.0 ns predicted by the error analysis. From the output-only modal analysis, the estimated modal parameters were found to agree well with that from the wired acceleration sensors. The phase angle of the cross spectral density of the two wireless accelerations showed that there was no apparent time-synchronization error observable. These observations indicated a successful operation of the proposed time-synchronization method.