Cheese whey, a byproduct of the cheese-making industry, is discarded in many countries in the environment, causing pollution. This byproduct contains high-quality proteins containing encrypted biologically active peptides. The objective of this work was to evaluate the suitability of using this waste to produce bioactive peptides by enzymatic hydrolysis with a digestive enzyme. Cheese whey from white cheese (Panela cheese) was concentrated to increase total protein and hydrolyzed with trypsin. A central composite design was used to find the best conditions of pH and temperature, giving the higher antioxidant capacity and Δ Angiotensin-converting enzyme inhibition (Δ ACEI) activity. Higher biological activities were found when hydrolysis was performed at 52 °C and a pH of 8.2. The maximum value for the 2,2- diphenyl-1-picrylhydrazyl (DPPH)-scavenging activity was 26%, while the higher Δ ACE inhibition was 0.89. Significant correlations were found between these biological activities and the peptides separated by HPLC. The hydrophilic fraction (HI) showed highly significant correlations with the antioxidant capacity (r = 0.770) and with Δ ACE inhibition (r = 0.706). Antioxidant capacity showed a significant positive correlation with 34 peaks and Δ ACE inhibition with 33 peaks. The cheese whey was successfully used as raw material to produce peptides showing antioxidant capacity and ACEI activity.