Previews Anime News Network (ANN) had three editors review the first episode of the anime: James Beckett praised the premiere for creating "an aesthetic and a tone [that is] worth caring" and the "thoughtful approach to otherwise seedy material", highlighting the weighty and purposeful animation, the editing providing high tension in its scenes, and Shuichi being an interestingly "flawed and messy character" that's neither "boring or outright despicable," Nick Creamer praised the series' presentation of "uncomfortably hormonal adolescence" through its "terrific layouts and character designs, [its] strong sense of oppressive summer atmosphere, and [its] general quasi-horror tone" but was critical of Claire Aoki being used as a "source of pure fanservice" and "an idol of beauty and terror than a human being", concluding that: "
Gleipnir is both visually enthralling and dramatically fascinating in its hormonal grindhouse way, and probably deserves at least a glance from any adventurous anime fans." The third reviewer, Theron Martin, praised the writing for keeping the series' concept from going over the top and highlighted the "dark and moody ambiance" and "strong musical score", but was unimpressed by the "character design aesthetic" and animation, concluding that: "On the whole, I can't seeing
Gleipnir blowing people away with what it does, but it puts together just enough appeal that I can give it a mild recommendation."
Series Fellow ANN editor Steve Jones placed
Gleipnir at number five on his top 5 best anime list of 2020, saying while not the "tightest-written story, and [this] isn't a gold star adaptation or anything," he called it "gross, uncomfortable, subversive, and sexually-charged in the best way possible", concluding that: "Although the adaptation concludes without any kind of finality, it left me eager to see how these two broken kids would continue to enable their mutual downward spiral, and I hope I'll be able to sing its praises again in the future." Allen Moody, writing for
THEM Anime Reviews, said: "I'm still not sure how I feel about this. Despite Claire's callousness, Claire's and Shuichi's actions are at least ostensibly (though sometimes debatably) motivated by necessity, and a strong bond begins to develop between them (there's some interesting jealousy at times too, when Shuichi lets anyone else "inside" him.) There are numerous things left unexplained just yet (though the show is somewhat less confusing on a second viewing), but I found it all surreal, perverse, and yet weirdly fascinating." ==Notes==