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In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">F</mi><mi mathvariant="sans-serif">Σ</mi></msub><mrow><mo>(</mo><mi>δ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo>;</mo><mi>h</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of normalized holomorphic and bi-univalent functions associated with Ozaki close-to-convex functions. We provide estimates on the initial Taylor–Maclaurin coefficients and discuss Fekete–Szegő type inequality for functions in this family.