Psalm 55:22 (54:23 LXX): ἐπίρριψον ἐπὶ κύριον τὴν μέριμνάν σου καὶ αὐτός σε διαθρέψει οὐ δώσει εἰς τὸν αἰῶνα σάλον τῷ δικαίῳ
1 Peter 5:7: πᾶσαν τὴν μέριμναν ὑμῶν ἐπιρίψαντες ἐπ᾽ αὐτόν ὅτι αὐτῷ μέλει περὶ ὑμῶν
EF: The preceding verse (1 Peter 5:6) uses the wording, τὴν κραταιὰν χεῖρα τοῦ θεοῦ, suggesting that the referent of 1 Peter 5:7 is Jehovah God, the same personal entity mentioned in Psalm 55:22.
Thomas R. Schreiner (NA Commentary on 1, 2 Peter, Jude): "Peter's words here remind us of Jesus' exhortation to avoid anxiety (Matt 6:25–34), and some even see an allusion to Jesus' words.⁹⁸ More probably, the allusion is to Ps 55:22. Psalm 55 fits nicely with Peter's theme, for the psalmist implored God to help him because the wicked were attempting to destroy him, and even his close friend had turned against him. Verses 4–8 express the anguish and torment he felt in the midst of such opposition. Again we see evidence that Peter considered the thematic context of the Old Testament when he alluded to it. We find the allusion in v. 22 (Ps 54:23, LXX), “Cast your anxiety upon the Lord, and he will sustain you” (epiripson epi kyrion ten merimnan sou, kai autos se diathrepsei)."
Mark Dubis (1 Peter: A Handbook on the Greek Text):
πᾶσαν τὴν μέριμναν ὑμῶν ἐπιρίψαντες ἐπ᾿ αὐτόν. This portion of verse 7 derives from LXX Ps 54:23 (ET 55:22): ἐπίρριψον ἐπὶ κύριον τὴν μέριμνάν σου
πᾶσαν τὴν μέριμναν. Accusative direct object of ἐπιρίψαντες.
Fronted for emphasis (along with ὑμῶν).
ὑμῶν. Subjective genitive.
ἐπιρίψαντες. Aor act ptc masc nom pl ἐπιρίπτω. This participle is best taken as attendant circumstance, taking on the imperatival force of ταπεινώθητε (RSV, NIV, TEV; see also 2:1 on Ἀποθέμενοι and 1:14 on συσχηματιζόμενοι). Alternatively, some take it as a participle of means (NET; Wallace, 340, 630).