<p>This paper aims to investigate the influence of multiplicative noise on the Schrödinger equation with a nonlinearity of Hartree-type <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\frac{1}{|x|^{b}}*|u |^{2})u\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo stretchy="false">|</mo> <mi>x</mi> <mo stretchy="false">|</mo> </mrow> <mi>b</mi> </msup> </mfrac> <mrow /> <mo>∗</mo> <mo stretchy="false">|</mo> <mi>u</mi> <msup> <mo stretchy="false">|</mo> <mn>2</mn> </msup> <mo stretchy="false">)</mo> <mi>u</mi> </mrow> </math></EquationSource> </InlineEquation>. Firstly, local well-posedness for the Cauchy problem is established by combining deterministic and stochastic Strichartz estimates. Then, based on an a priori estimate of the solution in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>, the existence of a global solution in energy space is presented. Finally, a blow-up solution in the focusing case is constructed. The new ingredient of this work is to obtain the global existence and blow-up phenomenon of a solution to the problem with Hartree-type nonlinearity.</p>