Fourier ptychography (FP) can be a promising technique for long-range and high-resolution imaging. In this work, we explore reconstructions with undersampled data for meter-scale reflective based Fourier ptychographic imaging. To reconstruct with under-sampling captures, we propose a novel cost function for FP phase retrieval and design a new optimization algorithm based on gradient descent. To verify the proposed methods, we perform the high-fidelity reconstruction of the targets with sampling parameter less than one. Compared to the state-of-the-art alternative-projectionbased FP algorithm, the proposed one can achieve the same performance but with much less data.