Matrix-valued Gegenbauer-type polynomials are investigated. The main results of the paper are stated in Sections 2 and 3. In Section 2 the matrix-valued weight functions \(W^{(\nu)}(x)\), which are analogues of the weight function for the Gegenbauer polynomials \(C^{(\nu)}_n(x)\) are introduced: \(W^{(\nu)}(x)= (1-x^2)^{\nu-1/2}W^{(\nu)}_{\mathrm{pol}}(x)\), where \[ \left(W^{(\nu)}_{\mathrm{pol}}(x)\right)_{m,n}=\sum_{k=\max\{0,m+n-2\ell\}}^m \alpha_k^{(\nu)}(m,n)C^{(\nu)}_{m+n-2k}(x), \]
\[ \alpha_k^{(\nu)}(m,n)=(-1)^m\frac{m!n!(m+n-2k)!}{k!(2\nu)_{m+n-2k}(\nu)_{m+n-k}} \frac{(\nu)_{m-k}(\nu)_{n-k}}{(m-k)!(n-k)!}\frac{m+n-2k+\nu}{m+n-k+\nu} \]
\[ \times (2\ell-m)!(n-2\ell)_{m-k}(-2\ell-\nu)_{k}\frac{2\ell+\nu}{2\ell!}, \] \(m,n\in\{0,1,\ldots,2\ell\}\) and \(n\geq m\). If \(m\geq n\) then \((W^{(\nu)}_{\mathrm{pol}}(x))_{m,n}=(W^{(\nu)}_{\mathrm{pol}}(x))_{n,m}\). In Theorem 2.2 the LDU-decomposition of the weight \(W^{(\nu)}(x)\) is explicitly given in terms of polynomials \(C^{(\nu)}_n(x)\). Two symmetric matrix-valued differential operators with respect to the weight \(W^{(\nu)}(x)\) are introduced in Theorem 2.3. In Theorem 2.4 a matrix-valued Pearson equations for the matrix weights \(W^{(\nu)}(x)\) are obtained. In Section 3 the properties of \(P^{(\nu)}_n(x)\) – matrix-valued orthogonal polynomials with respect to the weight \(W^{(\nu)}(x)\), which are called the matrix-valued Gegenbauer-type polynomials, are investigated. In Theorem 3.1 a Rodrigues formula for \(P^{(\nu)}_n(x)\) is established and the squared norm for it is found. Theorem 3.2 states that \(P^{(\nu)}_n(x)\) are eigenfunctions of the symmetric matrix-valued differential operators. The three-term recurrence relation for \(P^{(\nu)}_n(x)\) is obtained explicitly in Theorem 3.3. In Theorem 3.4 an explicit expression for the matrix entries of the matrix-valued polynomials \(P^{(\nu)}_n(x)\) in terms of scalar-valued Gegenbauer and Racah polynomials is given. In Section 4 and Appendices A, B and C statements of Sections 2 are proved and statements of Section 3 are proved in Section 5.