Dwarf galaxies are characterized by a very low luminosity and low mass. Because of significant accretion and ejection activity of massive black holes, some dwarf galaxies also host low-luminosity active galactic nuclei (AGNs). In a few dwarf AGNs, very long baseline interferometry (VLBI) observations have found faint non-thermal radio emission. SDSS J090613.77+561015.2 is a dwarf AGN owning an intermediate-mass black hole (IMBH) with a mass of M_BH = 3.6⁺₋₂⁵₃⁹ × 10⁵M and showing a rarely seen two-component radio structure in its radio nucleus. To further probe their nature, i.e. the IMBH jet activity, we performed additional deep observations with the European VLBI Network (EVN) at 1.66 and 4.99 GHz. We find the more diffuse emission regions and structure details. These new EVN imaging results allow us to reveal a two-sided jet morphology with a size up to about 150 mas (projected length ∼140 pc) and a radio luminosity of about 3 × 10³⁸ erg s⁻¹. The peak feature has an optically thin radio spectrum and thus more likely represents a relatively young ejecta instead of a jet base. The EVN study on SDSS J090613.77+561015.2 demonstrates the existence of episodic, relatively large-scale, and powerful IMBH jet activity in dwarf AGNs. Moreover, we collected a small sample of VLBI-detected dwarf AGNs and investigated their connections with normal AGNs. We notice that these radio sources in the dwarf AGNs tend to have steep spectra and small linear sizes, and possibly represent ejecta from scaled-down episodic jet activity.