The Invisible Man is narrated in a realist style even though the actual events of the novel are quite fantastical and far-fetched. In this sense, Wells lives up to what Joseph Conrad called him in a fan letter: a "realist of the fantastic."
His style is typical of realism in the sense that he describes minute details that are realistic. Narrating the details of the non-glamorous struggles of the Invisible Man to get food and shelter make Griffin's situation seem a bit more tangible to readers. Wells frequently utilizes specific names for places, like Oxford Street or Port Burdock, rather than vague descriptions. Real places (like Oxford Street) and fictional places (like Port Burdock) are invoked with the same level of authority.
At the same time, Wells's style also pushes the boundaries of reality. Unlike the novel's specific and realistic description of various details related to the narrative's setting and circumstances, the Invisible Man himself is described indirectly and with words that appeal to the reader's imaginative power. Occasionally, Wells uses elaborate similes to show that an invisible man is something inherently grotesque and unnatural. The Invisible Man is explicitly described as "strange" and "terrible." Doctor Kemp gives a whole speech about how impossible and fantastic invisibility is in humanity, even though it occurs in the mysterious creatures of the sea. All these vague ways of describing Griffin while leaving his presence mostly up to the imagination have the effect of painting him as something out of the norm.
The novel's mixture of a very normal style and a more fantastical style ultimately makes the fantastic elements feel more believable while still preserving a sense of the bizarre.
