Investigating the identity, distribution, and evolution of bird species is important for both biodiversity assessment and environmental conservation. The discrete wavelet transform (DWT) has been widely exploited to extract time-frequency features for acoustic signal analysis. Traditional approaches usually compute statistical measures (e.g., maximum, mean, standard deviation) of the DWT coefficients in each subband independently to yield the feature descriptor, without considering the intersubband correlation. A new acoustic descriptor, called the local wavelet acoustic pattern (LWAP), is proposed to characterize the correlation of the DWT coefficients in different subbands for birdsong recognition. First, we divide a variable-length birdsong segment into a number of fixed-duration texture windows. For each texture window, several LWAP descriptors are extracted. The vector of locally aggregated descriptors (VLAD) is then used to aggregate the set of LWAP descriptors into a single VLAD vector. Finally, principal component analysis (PCA) plus linear discriminant analysis (LDA) are employed to reduce the feature dimensionality for classification purposes. Experiments on two birdsong datasets show that the proposed LWAP descriptor outperforms other local descriptors, including linear predictive coding cepstral coefficients, Mel-frequency cepstral coefficients, perceptual linear prediction cepstral coefficients, chroma features, and prosody features. Furthermore, the proposed LWAP descriptor, followed by VLAD encoding, PCA plus LDA feature extraction, and a simple distance-based classifier, yields promising results that are competitive with those obtained by the state-of-the-art convolutional neural networks.