For a probability measureµ on Ω and square integrable (Hilbert space) operator valued functions {A∗t}t∈Ω, {Bt}t∈Ω, we prove Grüss-Landau type operator inequality for inner product type transformers∣∣∣∣∣∫ Ω AtXBt dµ(t) − ∫ Ω At dµ(t)X ∫ Ω Bt dµ(t) ∣∣∣∣∣2η 6 ∣∣∣∣∣∣ ∣∣∣∣∣∣ ∫ Ω AtA ∗ t dµ(t) − ∣∣∣∣∣∫ Ω A∗t dµ(t) ∣∣∣∣∣2 ∣∣∣∣∣∣ ∣∣∣∣∣∣ η(∫ Ω B∗tX ∗XBt dµ(t) − ∣∣∣∣∣X∫ Ω Bt dµ(t) ∣∣∣∣∣2)η, for all X ∈ B(H) and for all η ∈ [0, 1]. Let p > 2, Φ to be a symmetrically norming (s.n.) function, Φ(p) to be its p-modification, Φ(p) ∗ is a s.n. function adjoint to Φ(p) and ||·|| Φ (p)∗ to be a norm on its associated ideal C Φ (p)∗(H) of compact operators. If X ∈ C Φ (p)∗(H) and {αn}∞n=1 is a sequence in (0, 1], such that ∑∞ n=1 αn = 1 and ∑∞ n=1 ||α−1/2n An f ||2+||α−1/2n B∗n f ||2 < +∞ for some families {An}∞n=1 and {Bn}∞n=1 of bounded operators on Hilbert spaceH and for all f ∈ H , then∣∣∣∣∣∣∣∣∣∣ ∞∑ n=1 α−1n AnXBn − ∞∑ n=1 AnX ∞∑ n=1 Bn ∣∣∣∣∣∣∣∣∣∣ Φ (p)∗ 6 ∣∣∣∣∣∣ ∣∣∣∣∣∣ √ ∞∑ n=1 α−1n |An|2 − ∣∣∣∣∣ ∞∑ n=1 An ∣∣∣∣∣2 X √ ∞∑ n=1 α−1n |B∗n|2 − ∣∣∣∣∣ ∞∑ n=1 B∗n ∣∣∣∣∣2 ∣∣∣∣∣∣ ∣∣∣∣∣∣ Φ (p)∗ , if at least one of those operator families consists of mutually commuting normal operators. The related Grüss-Landau type ||·|| Φ (p) norm inequalities for inner product type transformers are also provided