A control device for an engine in which partial compression-ignition combustion is executed within at least a part of an operating range of the engine, the partial compression-ignition combustion including spark ignition combustion and compression ignition, the spark ignition combustion being to be performed by combusting a portion of a mixture gas inside a cylinder by spark ignition and followed by the compression ignition combustion, the compression ignition combustion being to be performed by causing the remaining mixture gas inside the cylinder to self-ignite, the control device comprising: an in-cylinder pressure sensor configured to detect pressure inside the cylinder; and a combustion controller configured to control the combustion inside the cylinder during the partial compression-ignition combustion based on the detected pressure of the in-cylinder pressure sensor and a reference value defined as an upper limit regarding the noise, wherein the combustion controller is configured to control the combustion inside the cylinder during the partial compression-ignition combustion based on a combustion noise index value identified by the detected pressure of the in-cylinder pressure sensor and the reference value, the reference value is defined as an upper limit of the combustion noise index value, the combustion controller is configured to obtain a margin (y) from a history of the combustion noise index value acquired previously and based on a variation of the combustion noise index value acquired previously, and determine a final reference value (Wx) of the combustion noise index value by subtracting the margin (y) from the reference value of the combustion noise index value, the margin (y) corresponds to a standard deviation of combustion noise index values accumulated in the past over a given period, and the combustion controller is configured to determine a target start timing (θci) that is a target start timing or crank angle of the compression ignition combustion as a timing at which the combustion noise index value is equal to or less than the final reference value (Wx), and control the combustion inside the cylinder so as to achieve the determined target start timing (θci), wherein the reference value is adapted to increase as a vehicle speed, an engine speed, and/or an engine load increases. an in-cylinder pressure sensor configured to detect pressure inside the cylinder; and a combustion controller configured to control the combustion inside the cylinder during the partial compression-ignition combustion based on the detected pressure of the in-cylinder pressure sensor and a reference value defined as an upper limit regarding the noise, wherein the combustion controller is configured to control the combustion inside the cylinder during the partial compression-ignition combustion based on a combustion noise index value identified by the detected pressure of the in-cylinder pressure sensor and the reference value, the reference value is defined as an upper limit of the combustion noise index value, the combustion controller is configured to obtain a margin (y) from a history of the combustion noise index value acquired previously and based on a variation of the combustion noise index value acquired previously, and determine a final reference value (Wx) of the combustion noise index value by subtracting the margin (y) from the reference value of the combustion noise index value, the margin (y) corresponds to a standard deviation of combustion noise index values accumulated in the past over a given period, and the combustion controller is configured to determine a target start timing (θci) that is a target start timing or crank angle of the compression ignition combustion as a timing at which the combustion noise index value is equal to or less than the final reference value (Wx), and control the combustion inside the cylinder so as to achieve the determined target start timing (θci), wherein the reference value is adapted to increase as a vehicle speed, an engine speed, and/or an engine load increases.