TASEH (Taiwan Axion Search Experiment with Haloscope) devotes to search dark matter axions based on a haloscope setup, consisting of a frequency-tunable microwave cavity detector in a strong magnetic field and a signal receiver. The TASEH experiment targets axion searches in the mass range of 10–25 μeV, roughly corresponding to the frequency band of 2.5–6 GHz. In this presentation, we will describe our first physics search, which excludes values of the axion-photon coupling constant above 8.1 × 10^-14 inverse GeV, a factor of 11 above the KSVZ benchmark model, in the mass range of 19.4687–19.8436 μeV. We will also illustrate our subsequent efforts on improving the detection sensitivity up to the QCD axion-photon coupling limit, including developing a large-volume conic shell-cavity detector and integrating a quantum-limited Josephson parametric amplifier to the readout chain.