Abstract In this paper, a novel strapdown stellar-inertial guidance scheme is developed to correct the velocity and position navigation errors for responsive launch vehicle. Three types of error sources consisting of initial localization and misorientation errors, inertial sensor errors and gravity computation errors due to position navigation errors are discussed. The digital platform error model arising from initial localization and misorientation errors and gyro measurement error is derived. The detailed analysis for the velocity and position navigation errors caused by initial position errors, digital platform errors, accelerometer measurement error and gravity computation errors is performed. For the gravity computation errors due to the position navigation errors, an effective first-order approximation compensation scheme is addressed. A dual star correction strategy scheme is presented to estimate the error parameters and correct the cumulative velocity and position navigation errors. Compared with traditional stellar-inertial guidance algorithm based on nominal trajectory data and priori subsystem error statistics, the proposed algorithm uses the real-time trajectory data to calculate the function matrices used in the navigation error propagation equations. Thus, the corrections for velocity and position navigation errors are provided by the stringent navigation error model rather than the statistics of the subsystem errors caused by individual error source. Numerical examples are given to analyze the effects of the individual error factor with respect to the accuracy of strapdown INS and compare the navigation performances for all-inertial, stellar-inertial, and stellar-inertial plus gravity compensation guidance schemes.