This paper presents a programmable ultra-low-frequency relaxation oscillator for neuromorphic network applications. The oscillator adopts a 250 pA charging current to achieve ultra-low oscillation frequency and utilizes a subthreshold-region current mirror to realize negative differential resistance. The frequency of the proposed oscillator is configurable from 3.49 Hz to 31.1 Hz. The power consumption of a single oscillator is 24 nW with an area occupation 0.05546 mm$^2$. The design is fabricated in 130 nm CMOS technology with 3.3 V supply voltage. The functionality of the proposed design is proven with measurements.