Amylase (EC 3.2.1.1) enzyme has gained tremendous demand in various industries, including wastewater treatment, bioremediation and nano-biotechnology. This compels the availability of enzyme in greater yields that can be achieved by employing potential amylase-producing cultures and statistical optimization. The use of Plackett–Burman design (PBD) that evaluates various medium components and having two-level factorial designs help to determine the factor and its level to increase the yield of product. In the present work, we are reporting the screening of amylase-producing marine bacterial strain identified as Bacillus sp. H7 by 16S rRNA. The use of two-stage statistical optimization, i.e., PBD and response surface methodology (RSM), using central composite design (CCD) further improved the production of amylase. A 1.31-fold increase in amylase production was evident using a 5.0 L laboratory-scale bioreactor. Statistical optimization gives the exact idea of variables that influence the production of enzymes, and hence, the statistical approach offers the best way to optimize the bioprocess. The high catalytic efficiency (kcat/Km) of amylase from Bacillus sp. H7 on soluble starch was estimated to be 13.73 mL/s/mg.