Abstract The discrete generalized Cesàro matrix A t = ( a n k ) $A_{t}= ( a_{nk} ) $ is the triangular matrix with nonzero entries a n k = t n − k / ( n + 1 ) $a_{nk}=t^{n-k}/ ( n+1 )$ , where t ∈ [ 0 , 1 ] $t\in [ 0,1 ] $ . In this paper, boundedness, compactness, spectra, the fine spectra and subdivisions of the spectra of discrete generalized Cesàro operator on ℓ p $\ell_{p}$ ( 1 < p < ∞ $1< p<\infty$ ) have been determined.