Attaining information corresponding to the microseismic source location helps in understanding the reservoir fracturing process. Time-reversal-based migration methods are widely used to obtain a source image directly. Such source-locating methods share a fundamental weakness: The accuracy of the source image depends highly on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used in microseismic data to include an optimization of the source image and velocity model, simultaneously. However, such inversions are vulnerable to cycle-skipping problems, more so when the source location and source origin time are unknown. The computational cost of FWI is also high. To solve these problems, we have developed a source-focusing function as an additional objective to optimize the velocity model and source image. This objective function used to measure the source-image focusing property is defined by the estimated source-location coordinate and the source image. The source image is poorly focused if the velocity is inaccurate, and the objective function reaches a minimum when the velocity is accurate. We use the geometric-mean imaging condition to get a high-resolution source image at each iteration. Then, we use this source image to calculate the estimated source-location coordinate and the gradient of the objective functional with respect to the velocity. The optimized velocity can improve the source-image quality. In the end, the final output velocity and source image will allow us to fit the objective for all these attributes of the model and source image. Using synthetic data generated from the 2D Marmousi and the 3D overthrust models, we highlight the cycle-skipping immune and high-resolution features of our method. The application to field data also indicates that our method can improve the velocity model and source-image quality.