A 2 × 2 factorial feeding experiment was conducted to examine the effects of varying the maturity level of the grass used to prepare silage and the nature of concentrate starch source and their interactions on dry matter intake (DMI), diet digestibility, energy corrected milk (ECM) production and milk composition in dairy cows. Twenty-eight multiparous Swedish Red dairy cows, 133 ± 45 days in milk (DIM), with an average milk yield of 30 ± 4 kg/day and a live weight of 624 ± 69 kg were blocked by DIM and randomly assigned to seven replicated balanced 4 × 4 Latin squares with four 21-day experimental periods. The experimental diets consisted of four total mixed rations (TMR) consisting of early-cut grass silage (EGS) supplemented with either barley- or maize-based concentrate and late-cut grass silage (LGS) supplemented with either barley- or maize-based concentrate. All TMR contained identical proportions of forage (51%) and concentrate (49%). Total tract digestibility was estimated by determining indigestible NDF (iNDF) concentrations in feeds and faeces and using iNDF as an internal marker. The feeds’ ruminal degradation parameters were determined using both in situ (nylon bag) and in vitro (gas production (GP)) techniques. Cows offered diets containing EGS had greater (P < 0.001) daily dry matter (DM) intakes, ECM yields and total tract digestibilities for DM and organic matter (OM), but these were not affected by the nature of the concentrate starch source. No interaction between the maturity of the silage and the nature of the concentrate starch source was observed for DMI, diet digestibility or ECM yield. Both grass silages and concentrates had similar rates of ruminal degradation of NDF when measured in situ. The in situ DM (P < 0.001) and starch (P = 0.001) degradation rates of barley-based concentrate were greater than those for maize-based concentrate. In vitro OM GP rates and extents were similar for both concentrate feeds. The results showed that diets containing EGS offered better animal performance and diet digestibility than diets containing LGS. The concentrate starch source did not affect animal performance, but total NDF digestibility was better with diet containing barley- than maize-based concentrate.