We have experimentally demonstrated a direct-detection (DD) 112-Gbit/s 16 quadrature amplitude modulation (QAM) transmission over single-span 140-km standard single mode fiber (SSMF) with Kramers-Kronig receiver and a sparse I/Q Volterra filter (VF). The sparse I/Q VF was proposed in our previous work and it is based on dual-input real-valued Volterra series and ℓ<sub>1</sub>-regularization method. In this paper it is used for compensating the nonlinear distortion in a short-reach DD optical 16-QAM signal transmission system. In back to back case, sparse I/Q VF represents the great compensation ability to the saturation effect of the electrical amplifiers and the nonlinear sinusoidal transfer function of I/Q modulator. It provides around 1-order magnitude improvement of BER when reducing 84% complexity from full I/Q VF. For fiber transmission case, sparse I/Q VF can mitigate the fiber nonlinearity effectively and it achieves single-span 140-km transmission at hard-decision forward error correction (HD-FEC) threshold of 3.8 ×10<sup>-3</sup> with less than half complexity of full I/Q VF. Besides, optical signal noise ratio (OSNR) performance at 120 km is measured and sparse I/Q VF reduces the required OSNR at HD-FEC threshold by 1.3 dB. In a word, we investigate the performance of sparse I/Q VF in short-reach optical 16-QAM transmission system and sparse I/Q VF reveals its potential in the growing short-reach applications, such as data center inter-connection and metropolitan area network.