Previous X-ray spectral analysis has revealed an increasing number of AGNs with high accretion rates where an outflow with a mildly relativistic velocity originates from the inner accretion disk. Here we report the detection of a new ultra-fast outflow (UFO) with a velocity of $v_{rm out}=0.319^{+0.005}_{-0.008}c$ in addition to a relativistic disk reflection component in a poorly studied NLS1 WKK~4438, based on archival ustar and suzaku observations. The spectra of both suzaku and ustar observations show an Fe~textsc{xxvi} absorption feature and the suzaku data also show evidence for an Ar~textsc{xviii} with the same blueshift. A super-solar argon abundance ($Z^{prime}_{rm Ar}>6Z_{odot}$) and a slight iron over-abundance ($Z^{prime}_{rm Fe}=2.6^{+1.9}_{-2.0}Z_{odot}$) are found in our spectral modelling. Based on Monte-Carlo simulations, the detection of the UFO is estimated to be around at 3$sigma$ significance. The fast wind most likely arises from a radius of $geq20r_g$ away from the central black hole. The disk is accreting at a high Eddington ratio ($L_{rm bol}=0.4-0.7L_{rm Edd}$). The mass outflow rate of the UFO is comparable with the disk mass inflow rate ($dot M_{rm out}>30%dot M_{rm in}$), assuming a maximum covering factor. The kinetic power of the wind might not be high enough to have influence in AGN feedback ($dot E_{rm wind}/L_{rm bol}approx 3-5%$) due to a relatively small column density ($12^{+9}_{-4}times10^{22}$~cm$^{-2}$). However note that both the inferred velocity and the column density could be lower limits owing to the low viewing angle ($i=23^{+3}_{-2}$$^{circ}$).
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