To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of O(n2). Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search. To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is an estimated by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, whereby its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an suitable grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of O (n2). Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate si milarly by grid search.