This is a brief, devotional-style piano piece by the American composer George Balch Nevin. Its distinctive character lies in its simple, hymn-like harmonic progression and accessible melodic line.
Focus on maintaining a smooth, singing melodic line against the accompanying chords.
Comparable difficulty and character — good candidates for what to learn next.
"Jesus, my Saviour! look on me." is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 3.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of "Jesus, my Saviour! look on me." lasts about 3 minutes.
"Jesus, my Saviour! look on me." is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Bohemian Melody by William Vincent Wallace, Berceuse by Aleksandr Ilyinsky, Andante en Sol Mayor by Julián Santos Carrión — see the full similar-pieces list on this page.